How do I find someone and start a relationship?

I'm a 21 year old male. I haven't had much luck with the opposite . I'm not really sure why. I have a lot of friends, both guys and girls. People say I'm nice. I think I'm good looking--my gay roomate told me when he was drunk and I work out and have a six pack. I also play guitar, b, cello, sing and write music. I'm pretty smart too--I go to an ivy league school. But I don't want to sound full of myself, in fact my self esteem is pretty low because nobody seems to want me. I try to be really out-going and go to parties etc. but I never really get anywhere. My friends talk about hooking up like it's a fun game. I don't really get that at all... I'm just kinda lonely and would like a companion. I don't understand. Is there something wrong with me? Do I just not know the rules? What should I do?