I'm a 20-year-old man and I have a crush on a 15-year-old girl. What should I do?
Less than a century ago you could have married her, so it is not as insane as people would like to describe. One answer was correct in that you have to abide by the rules of a society you live in. If you are interested in her for a life partner, you are also very young, then put in the time for a proper courtship. You may be friends with her family but you may not touch her until she is of legal age and can consent with full agency.
People on this thread are treating a twenty year old as if he were a forty year old. Twenty is still very young. Crushes between people from 15–20 happen all the time in both directions. It just so happens that she is not of age and you mustn't pursue that sort of relationship with her. You haven't mentioned whether she is even interested in you as a friend. If she thinks you are nice that is one situation. If you are stalking her in an unwanted sort of way that is entirely different. Do not do that, please.
Your choice is to wait for her, if you actually are even in the running for her attentions, or move on to someone closer in age that you can safely date.
The other thing implied here is that sex is a natural part of dating. It isn't. One can date a person without having sex with them. In fact one should do this if one is serious about a partner.
Having sex is easy. Being a life companion is the harder work. If she is your Miss Right, you must simply be a gentleman as long as is required. This is simple common sense and further, you should take time with anyone else you are interested in, if you want a lasting relationship.