So how do things like dating and relationships work?

[me]

You have put yourself in a predicament. It can be very difficult to transform a friendship with a girl into something more. But based on the information you've given, it seems like there could be something more there. You don't just assume she's your girlfriend because if she doesn't feel the same way things could get akward. You need to talk with her about it. Tell her how you feel about her. And here's why your in a predicament because if she doesn't feel the same way then you've probably lost your friendship. But if she does feel the same way (which I'll be she does) then you'll be all set. If you don't believe its worth the risk, then just remain friends and hope she makes a move on you.