How does conversion work in Buddhism? 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. 

Personally I like the view of Dzongsar Jamyang Khyentse Rinpoche who has written a book on the topic called "What Makes You Not a Buddhist":


  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).


If you want to mark your decision to become a Buddhist you can 'take refuge'. This ceremony or commitment can be found in many Buddhist traditions. More info also here

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).