Sufism is not a mixture of Hinduism and Islam, the closest thing to that is the Sikh faith in my opinion. Hinduism has many gods and is polytheism and Islam on the other hand is a radical monotheism, so there is a fundamental incompatibility here between Islam and Hinduism. However, this is not to say that the Hindu’s do not have some ideas beyond polytheism that are similar to the idea of deity in Islam, for instance there is the Nirguna Brahman, or the God Head that is somewhat similar to the idea of God in Islam. However, since SHIRK is the greatest wrong action in Islam, this philosophical similarity in some respects is dwarfed by the idea that there are other gods that are expressions of the Godhead in Hinduism, those beliefs are believed to be in fundamental error from the point of view of Islam, so there is no possibility of overt reconciliation between the two faiths. Islam is also iconoclastic in the extreme and this is another point on which there is a radical difference.
Also there is a fundamentally wrong premise in the question, that links Sufism with the mixture of Hinduism and Islam. Sufism against what its Salafi detractors might say is not in general engaged in either Shirk or Idol worship, or the asking for intercession through holy men within Islam. This also is a misconception fostered by the Wahabis. It is in fact the Salafis that are the heretical sect because they are Karaja, those who say it is alright to kill other Muslims. Sufi’s for the most part are Muslims that are interested in the meaning of the practices that they follow in Islam, and pursue them with more rigor than those who are doing these practices for outward reasons. Sufism is rooted in the three main tenets of Islam, Iman, and Ihsan. Sufism emphasizes Ihsan, inverse witnessing, i.e. God withesses you even if you do not witness Him, which includes the idea that what ever you witness is part of His witnessing, even though there is no connection between you and Him. What ever you witness is infinitely overwhelmed by God’s witnessing. And it is from that witnessing by God of our actions that meaning is generated for the practices of Islam and belief, i.e. Iman, is generated by this reciprocal witnessing. That is to say that we witness that our witnessing is overwhelmed by the witnessing by God of us and our actions. We could call this witnessing epiphanies of the manifestation of God, which are called Tajalliat (sending down of inspiration from God through knowledge and insight into his Sifat, or Qualities by which He is recognized and which are referred to by His myriad names.)
OK. Now that we have clarified the confusions that are inherent in the background of the question. We can go on to answer the specifics of the question.
We have already said that Sufism is merely a name for an emphasis on Ihsan, which is one of the three tenets of Islam which take together with Islam and Iman constitute the whole of religion, according to the Angel Gabriel who appeared as intersubjectively witnessed by the Mohammedan community in the prophet’s lifetime.
So the crux of the question left for exposition is how one can be a Sufi. And the answer to that is to pay attention to Ihsan and the meanings of the practices of Islam, not just to the beliefs and outward practices themselves. If you do that then you are a sufi in every sense of the word that is worthy of mention. That is of course a matter of personal attitude toward practice, and has nothing to do with anyone else than one self, necessarily.
But the road to doing that is immensely helped by reading about and understanding the admonitions of the great sufis throughout history. And it may be helped by keeping company with others who are similarly inclined. But since so much of what passes as Sufism, especially in the West has so little to do with the core of the matter, which is meaning, and witnessing of witnessing within practice, there is always a danger of getting caught up in a cult, or some other group that considers themselves to be Sufis, but are actually not following either the practices or have the correct attitude that would call forth the proper approach toward those practices centered on Ihsan. But the best way to recognize genuine Sufic teaching is to practice the core of it oneself within the auspices of Islam and Ihsan, and then hopefully that will give one a means of discrimination of genuine Sufism when one encounters it which is rare.
Another key point about Sufism is that it is more closely allied with Nondual religions like Buddhism, and Taoism than it is with anything in Christianity and Judaism. And so knowing something about Buddhism, Taoism and Nondual approaches in general will help in the recognition of genuine Sufism in others. Islam in general is a nondual heresy of the Western worldview, just as Buddhism is a nondual heresy with respect to Hinduism, and Taoism is a nondual heresy with respect to Confucianism. So this is another reason not to not mix up Islam with Hinduism. That is because it is more like the nondual heresy of Hinduism which is Buddhism. There are forms of Advaita Hinduism which is itself nondual, but they were based on Buddhism as reabsorbed into Hinduism though the auspices of Shankara who interpreted the Upanishads in a nondual way inspired by Nagarjuna’s exposition of nonduality which is one of the purist sources of the understanding of nonduality in any religion. Being a Western Heresy, even the Muslims and many Sufis interpret Islam dualistically and thus do not understand very well their own religion, which is better appreciated in light of global examples of nondual philosophies and religions rather than in comparison with either Christian or Judaic religions which are mostly monistic or dualistic rather than nondual. Nondual means the rejection of both monism and dualism. The radical twist that Islam produces on Judaic Monotheism is to apply a nondual approach to it, based on many insights derived from Quran and the sunnah of Muhammad.
As noted by Jami in the Precious Pearl the viewpoint of sufism is very different from that of either Muslim philosophy or theology. And that is because of the intuitive recognition by Sufis of the nondual strain that runs throughout Islam for those with Iman who can recognize the meaning of Ihsan, and they are rare. But the Sufic friends of God (Wahlia) have a long and noble tradition of resisting dualism and monism as the only way to relate to Islam for those with Iman. So another definition of Sufism the group of people who intuit the nondual nature of Islam within the practices and tradition of Islam itself, without any external basis for interpretation, such as Greek Philosophy and Theology. Unfortunately, Buddhism and Taoism have not been well understood by the Muslims who had Sufic inclinations, so the comparison was probably not made except by individuals who were either involved in Buddhism or Taoism prior to their conversion. Since these religions were seen as polytheistic and not distinguished from polytheisms by Muslim scholars this internal coherence between the various nondual ways has not been previously recognized. It is really only apparent to someone who is steeped in Buddhism and Taoism prior to conversion who can see clearly these linkages between nondual approaches to spirituality, and people who have this kind of fore-knowledge are also rare. So it is not widely known that these strains of similarity between all genuine nondual ways exists and can be used to interpret Islam, Ihsan and Iman the three tenants of the Western nondual heresy building on the Abrahamic tradition but turning it inside out by approaching it on the basis of nondual ways of thinking and acting.
So this brings us to another way to be a Sufi, which is to make non-nihilistic distinctions and to act in a way that is in concert with those nondual distinctions that one makes intuitively. Living a life engulfed by the wonder and awesomeness of nonduality permeating everything is tantamount to Sufism if it occurs within the limits of the practices of Islam and through the adherence to Ihsan. In this way Sufism is really little different from either Mahayana Buddhism especially that of Hua Yen, or Tien Tai, or even DzogChen, as long as one recognizes that sufism is even more radical than these in its pursuit of nonduality. Sufism posits even deeper non-dualities than any of these other essentially similar ways of approaching spirituality. Now when I say similar I do not mean that the practices or beliefs have anything in common, nor is the goals of these various spritualities the same. But what is the same is the nondual approach to life and spiritual practices, and that came from a fundamental rejection of dualistic and monistic ways of approaching spirituality.
Now what is nonduality as an approach. It is very simple it says Not One! Not Two! but something else beyond what can be approached via logic and though either concepts or experiences. The best example of this in the West is the teaching of Meister Eckhart. In Hinduism the nearest thing is Advita Vedanta founded by Shankara or the Buddhism of Nagarjuna. In China it is expressed in Taoism, and Chinese Buddhism. Basically the way to think about it, is to take the Tetralemma which originated with the Buddha, supposedly according to Pali scriptures which says that Emptiness is something other than A, non-A, both A and non-A, neither a nor non-A. In other words the for logical operators and, or, nand, nor are surpassed in some aconceptual, aperceptual (as in apperception), aexperiential way. The nondual is neither a monism nor a dualism, nor a polytheism. Any dualistic or threefold, or higher fold distinction that you can make nonduality is always pointing back to a state prior to the arising of those distinctions. Plato called this non-representable intelligibility. Plato understood it very well, and it is in fact behind his use of irony. And in fact we can claim that Plato is the source of this kind of understanding in our tradition if read from a nondual perspective. Once you realize that there is an absolute limit to what the mind can comprehend and one orients toward that which surpasses all understanding, such that one cannot make dualistic distinctions (A monistic distinction is one in which the other myriad distinctions have been suppressed in favor of one particular alternative.) So in the sense that YHWH is seen as the God of the Jews and is differentiated from other gods of polytheism, then this is a monism. But Allah claims to be prior to the arising of all other gods, and his oneness is not conditioned by the one and the many of things. Tawhid is not oneness in relation to other numbers of things, but rather primordial uniqueness where there is no other to be compared or contrasted to. Tawhid is like Kant’s idea of the Singular as being the dialectical synthesis of Unity and Totality. Allah is claiming to be Singular in a primordial sense, i.e. prior to the creation of all existent things, including other gods created by men that obscure the Haqq (Right/Debt/Truth). However, the difference between primordial uniqueness and singularity of something like spacetime is that Tawhid points back or indcates the primordial uniqueness prior to and after all things, beyond either what is in-timespace or eternal, and every other duality or more complex sets of distinctions. In this sense radical monotheism is one that rethinks the One God as the primordial ground out of which everything we know as existing comes and which sustains all things, and which is where they will return on dissolution, and in this sense it is like the idea of the Nirguna Brahman, or like the Godhead described by Meister Eckhart.
Thus it is possible to use Buddhism and Taoism to critique Sufism, and Sufism to understand more fully Buddhism and Taoism in terms of the differences between these nondual approaches sustained in their own traditions. Many Cristian heresies came into Islam and mixed into Sufism in the East. So there are many practices of people who consider themselves sufis which really were spawned out of dualistic heretical constructs that reacted to Catholic Dogmatism and were forced to flee into Islam by the Inquisition. So there is a perspective that recognizes the similarity of all nondual ways, which then can critique the dualistic anachronisms within those nondualistic traditions, where they fell back into dualism or monism and were not true to their own insights, because nondual approaches are hard to hang onto. Sufism as a tradition is synchronistic, as was Buddhism and Taoism once they became traditions in their own right. Thus we must carefully separate dualistic or monistic intrusions into these traditions. But if we have a strong grasp on the meaning of nonduality as the axiom Not One! Not Two! Not Many! but some other matter or ground prior to any distinctions arising which engulfs all distinctions, then we will be able to differentiate the true insights of these various nondual traditions as they have accreted historically. What is ironic is that the engulfing of conventional or ungrounded distinctions by nonduality, allows one to make non-nihilistic distinctions. This is because that ground prior to distinction is precisely the place that nihilism ultimately takes you if you are disillusioned enough with monisms (dogma or ideological totalitarianisms) or dualisms, or polymorphisms of any kind. To have a monism a dualism has to arise and then one of the duals must be suppressed, but it can never be suppressed completely and it always haunts the monism.
So in a way the best way to practice Sufism is to know something about Buddhism and Taoism and to look for that which it has in common with these other nondual ways and then to pursue that with as much focus as one can muster. Knowing something about DzogChen, Hua Yen and Tien Tai Buddhism cannot hurt either because they point beyond Buddhism and Taoism to something deeper that Sufism is also pursuing. The nice thing is that these sources are pretty much independent historically, and thus the cross contamination is minimal except for early attempts of the Chinese to understand Buddhism via Taoism. Because these different approaches to nonduality are rooted in different traditions it is easy to see what is similar between them and thus be sure that this is the genuine aspect of nonduality which is not contaminated by the later introduction of anachronistic dualisms implicitly.
The main difference between Sufism and the other nondual traditions is that Sufism is based on revelation, while the others are not in any overt way. And this is also helpful because one can surmise how far purification of the self can go without dependence on revelation, and what is contributed by revelation to that nondual approach.
Now there is also something else implicit in the question that needs to be addressed. You say What IS Sufism. How can I BE a Sufi. Strictly speaking you cannot BE anything except in the projection of illusions. Being only exists in Indo-European languages. Buddhism is specifically a rejection of Being though the concept of Anatman. And Chinese and Arabic are non-indo-european languages. So Being is not only something you cannot be, but itself is merely an illusion and to the extent you ARE anything it is an illusion. Buddhism, Taoism and Sufism talk about Existence. In Arabic Existence is what is found without any A priori or later projections. I.e. there is not any reading back of our own projections out of phenomena, which is the nature of illusion. However, for us Whatness as essence or natural kind is caught up in Being which provides the substrata or substance for the attributes of a species. By primordial ground we do not mean this substance which is imagined as an illusory continuity though the idea of Being. To truly, really exist as the same as a Sufi, Buddhist or Taoist is the most you can hope for beyond the presence and absence of phenomena, i.e. the visible and invisible, and any other duality. Aspects Truth, Reality, Identity and Presence are shared by Being and Existence. However, these aspects are beyond being fused or separated in nondual manifestation which is beyond existence. So the most you can hope for from any nondual tradition is to exist within a nondual state for as long as you can sustain it. You cannot be, essentially, a Sufi, and Sufism has no whatness in the normal sense of an essence which constrains and connects attributes that pervade something particular based on the substrate of Being. We exist with other created things, but God manifests. And it is that manifestation that defines His witnessing that encompasses our witnessing. When we say that existence as Wajud is what is found, then we mean what is found by God, not our finding of other things. Prophets are the ones who are found by God and who have epiphanies of His manifestation (sifat), like Moses for instance.
So hopefully this will help you orient toward Sufism. Don’t become a Sufi, or Buddhist, or Taoist, or one of their dualistic counterparts, but become a Nondualist recognizing the truth of the axiom Not One! Not Two! Not Many! and you are most of the way there, then it is must a matter of learning more about the tradition of nonduality that you are included towards. Acceptance of Music, Arts, and the emphasis on the exclusiveness of the Love of God are just outward manifestations of a much deeper reality and truth. Sufis are not swayed by outward differentiations of things, but only the inward non-nihilistic distinctions he can make based on the recognition of the most fundamental and radical (root) nonduality.
In Islam this axiom appears as the Shahada which states that: There is no god but Allah. And the Prophet is His messenger. In order to try to prove the case that I have been making lets think about this axiom as it appears in Islam. The gods of polytheism, or even monism of monotheism as separate things do not exist but only Allah manifests. In other words there is an indication of a Primal Ground of all things beyond existence, and that is given a specific and unique name, as well as other names that is a specific signature which make clear the sifat of Allah, i.e. the ways in which He manifests. He indicates the “essence” of Allah that holds together yet separate His “attributes”. However, these are Greek philosophical ideas that differentiate Essence and Attributes, and thus are suspect, so it is better to stick to the Arabic terminology. The so called Essence of God, i.e. the Godhead is called the Dhat in Sufism. Yet to the extent that we think there is a distinction or duality between Sifat and Dhat that is a cognitive mistake.
There is no god, only Allah.
Notice that god is singular, but implicitly suggests the many gods of polytheism that can be different and represented by idols. The commandment is that you shall have no other god before me. The operative word here is BEFORE. In other words any god that you can name or represent is after the primordial ground has been split by the first distinction. God as Ground of everything in manifestation prior to and exclusive of existence really cannot be associated with anything else, because in the that pristine pre-creation state which “exists as it did exist” there were no distinctions between things Other than Allah the unique and singular root of all things to which they return. So the first part of the Shahada can be linked to a statement of nonduality, because Allah manifests continually prior to, during, and after the existence that we perceive. And any god that we might conceive did not exist in that primal ground of all things to which all things return. This is essentially the idea of the Godhead of Meister Eckhart and Nirguna Brahman of the Hindus. Major place where this view is expressed is the Isa Upanishad.
Now the other part of the Shahada I left as Prophet because we can generalize and talk about any Prophet in their time as the one who is mentioned in the second part of the statement. The Prophet being the messenger of the Haqq to mankind, essentially is brining our attention to that nondual ground prior to all existence and after all existence not to mention both in-time and endless time. The primal ground is out-of-timespace. There is no pantheism, because from the point of view of the Absolute, the illusion of Being and the existence of created things never really happened. All that really and truly happened in Haqq was manifestation that engulfed and overwhelmed actual existence and the illusions of Being. What manifests is recognized to have necessary existence but that is just a side effect of manifestation with respect to existing things.
So the idea that we can get messages from the Primal Ground as it manifests as Absolute Spirit (Angel Gabriel) via other human beings that are part of our community is a fundamental recognition that human beings can be enveloped, overwhelmed, engulfed, awe struck, and immersed in that Primal Ground themselves without any mixture of transcendence and finitude (i.e. the normal duals we attribute to God probably wrongly). So what ever prophet’s name as a unique human being you want to plug into the Shahada, it is a fundamental recognition that this type of communication directly from the Ground of the Haqq is possible, and actually occurred in history. In other words there is historical grounds for what Hegel calls the advent of Pure Spirit and both the advent of Jesus as penultimate Prophet and Muhammad as last Prophet are just two examples of this kind of intrusion into history, not of the transcendent into finitude, but of the deepest possible nondual into the heart of unique human beings that come as messengers occasionally throughout human history. Thus if we apply the Hegelian idea of the intrusion of Absolute into history via human beings, as what makes us human together, then we get an amazing reading of the history of the nondual heresy of Islam with respect to the dualistic Western worldview which it challenges even within the historical interpretations of Islam by Greek trained intellectuals that resulted in dualistic philosophies and theologies.
So ultimately in some sense not only can you not BE as Sufi but all the nondual ways call into question your ultimate existence as a self, not to mention an ego, transcendental or otherwise. So from a nondual position you cannot be anything because you do not exist, necessarily but only accidentally as an aggregate of Tattvas or Dharmas in the sense of Heraclitian flux. You exist as a non-unified and non-total aggregate from that perspective. However, you are singular to the extent you are embedded in the singular timespace though your embodiment which is finite. However, you are whole which is the nondual between unity and totality as extremes to the extent you are a negentropic organism that is viable. And also strangely enough you belong to a worldview which is radically dualistic but cannot avoid having a nondual kernel beyond its nihilistic core, where the core is taken to be Logic which constrains rational logos, and the nihilism is that all sorts of nonsensical statements can be rendered logical in symbolic logic. But there are discontinuities between the logical operators and, or, nand, nor, and though this discontinuity logic is fragmented, and points toward the nondual of emptiness inwardly at the core of awareness. Non-dual emptiness is the antidote to nihilism, and once this homeopathic antidote is taken then the miasma of nihilism is cured, and we are able to make non-nihilistic distinctions even in this most nihilistic of all worldviews. So much so that it is willing to destroy the entire worth just to spite itself. The only way to allay that almost certain destruction of our earth by our now dominant worldview is though nondual transformation of ourselves via nondual ways of approaching our human existence which is now threatening the existence of not just other species but also itself.