I am a Hindu, but I like Buddhism. How does that work? Does one need to convert to practice Buddhism? If so, how does one convert to Buddhism? Can anyone convert to Buddhism? Or can I just practice without converting?
First of all, there isn't one agreed upon definition about when you are truely a Buddhist. Some people say you are a Buddhist if you consider yourself to be one, others say you need at least several years training from an acknowledged Buddhist teacher.
It’s whether you agree with the four fundamental discoveries the Buddha made under the Bodhi tree, and if you do, you can call yourself a Buddhist (ref).
Anyone can become a Buddhist or you can just practice without any formal conversion. You do not need to give up Hinduism. To quote Khenpo Kartar Rinpoche:
... it is not necessary to give up any religious affiliation to practice Buddhism unless that religion demands actions that contradict Buddhist principles. .... Also, it is not generally necessary to change your diet, dress or relationships, though some people choose to do so. (ref).
Ceremonially, you can take Refuge. In many traditions, this is the entry or acknowledgement of being dedicated to being a better person.
Kagyu.org has this very nice talk from Kalu Rinpoche about what taking Refuge is and the Three Jewels: http://www.kagyu.org/kagyulineage/buddhism/bec/bec04.php
It finishes with this wonderful thought:
It should be understood that the taking of refuge is not a process whereby the Buddha takes those who appear to have devotion to him and leads them to his side. Through taking refuge, one begins a process oneself which, going through various stages, will lead to one's own realization of the same state, the same experience as the Buddha.
And I believe Buddhism is open to all, with some gray areas around the insane and mentally handicapped. If you are not in "your right mind", it is difficult to understand deeply what Buddhism is. That is probably a different question though.
Conversion into Buddhism from a Zen Buddhist perspective, initially requires the initiate to take refuge into the “Triple Jewels” in a formal ceremony headed by a religious leader.
The “Triple Jewels” consist of three things: the Buddha, the Dharma, and the Sangha.
This link on Buddhism Stackexchange explores the nuances of “taking refuge” into the “Triple Jewels” from various Buddhist perspectives.
In Zen Buddhism, which includes the Mahayana Buddhist traditions of East Asia the following vows for taking refuge are used:
I take refuge in the Buddha, wishing for all sentient beings to understand the great Way profoundly and make the greatest resolve.
I take refuge in the Dharma, wishing for all sentient beings to delve deeply into the Sutra Pitaka, causing their wisdom to be as broad as the sea.
I take refuge in the Sangha, wishing all sentient beings to lead the congregation in harmony, entirely without obstruction.
After the initial ceremony, the initiate follows the basic tenets of Buddhism by applying them to their circumstances along with various forms of meditation. However, the Zen Buddhist tradition generally considers the terms: Buddhist, Buddhism, and Triple Jewels as methods to help the initiate along the path to enlightenment but are not an end in themselves.1 So, converting to Buddhism from the Zen Buddhist tradition is more about starting a life long process rather than being a member of an in-group versus an out-group.
- Buddhism Plain and Simple by Steve Hagen
It depends. I suggest you study the essential points of Buddhist teaching, especially the teaching on the three characteristics of impermanence, unsatisfactoriness, and non-self, and the teaching on dependent origination. These teachings are incompatible with some ideas in Hinduism (Hinduism is very diverse, so I don't think there is always contradiction.)
The main ideas that are common in Hinduism which conflict with Buddhism is the teaching of Brahman, an absolute reality which all of the world derives from. That doesn't fit, and it would also be problematic if you believe that the Gods are eternal beings who have always existed and always will exist. However, if you just have love for the Gods and feel devotion towards them and preform Pujas to them, from a Buddhist perspective there is nothing intrinsically wrong with that. In the time of the Buddha people venerated all sorts of beings, even including Yakshas and Nagas and the Buddha never spoke against it or forbade his followers from it, and in South East Asia today, some Hindu Gods (such as Brahma and Ganesh) are worshiped by faithful Buddhists and no one thinks there's a problem with it.
If you don't feel a contradiction, by all means, consider yourself to be both a Buddhist and a Hindu. The Buddha himself had lay followers who where Brahmin priests and it wasn't a problem.
Buddhism is by practice. There is no conversion.
When you take refuge in the Triple Gem you take refuge in the qualities of Buddha, Dhamma and Sanga through this now has turned into a ceremonial outlook.
You can call your self a Christian, Muslim, Hindu, etc. but still practice Buddhism as at the core of the Buddhist practice is Vipassana. This can be done by any one.