I think you should hang out with this girl more often if you don't already. If you're uncomfortable maybe make it a group thing but don't invite people who you think will become competitors for this girl's affection. After a couple nights out you should work up the courage to do a one-on-one thing. If you don't know where to go maybe you could take her someplace that she really enjoyed hanging out at before and you guys could explore that area a little more.
You could also get to know one of her friends pretty well (which should be easy if you aren't attracted to this friend) and get to this girl through him/her. Should be a girl though cause guy friends would probably be defensive. If you feel comfortable you could tell this friend about your feelings, but don't ask them to tell the girl for you that'll be a turnoff. If they do tell the girl let it be their decision.
A hook up is a simple way to get things started. Sometimes it's easier to kiss a girl then to ask a her to be your girlfriend. Wait for the right time when you're alone together. You can experiment intimacy and then see where it goes from there. Just hang out if all you want is companionship, friendship, but you're gonna have to hookup if you want to be a real couple, I think.