How do I become friends with her?

There's this girl I have to hang out with a lot because of school and activities outside of school... but she doesn't exactly like me. When it's just the two of us, she talks to me a little, but I'm usually hanging out with her with her friends which is awkward... so I would appreciate knowing how to make good friends with her. She's also one of those people where if you are on their bad side... not good. So, at risk of sounding like a typical teenage girl... How do you make good friends with the popular girl?

Additional Details: I'm "that kid." The girl who wears weird stuff but isn't scene/ emo or whatever they call it. On a scale of 1-10, I am a 6 on the popularity scale... MAYBE a 7. I'm good with people if I spend individual time with them and if they are somewhat open minded... the girl is pretty typical. I feel like she may kind of want to be friends with me, but since I'm "that kid" she'd rather not associate any more than she has to with me.

That's difficult to answer without clearly understanding what you're trying to accomplish. If she's the "leader of the pack," recognise that with comments like, "How did you become so popular?" or, "I'd like to be like you." That will let her know you are no challenge to her "authority." Don't do anything that will make you appear to be in competition with her.

If you're fun to be with, she doesn't feel any competition plus all of the normal elements to good friendship like being honest, fair and loyal, you may be able to make the transition from "that kid" to "The Kid."