Stop putting her on a pedastool. As long as you are "not the best looking guy in the world" and she is "one of the popular people" you will always be her "underling"--a SERVANT to her and her whims.
This is going to make you try to do "nice" things to "win" her over. You'll try to be a gentleman and all that mumbo jumbo, and what you are going to find is that she is going to ditch you for a guy who treats her like CRAP.
So you need to remove the thinking that she is somehow better than you. Why? Why is she so much better than you? Because she has more people around her than you? That's crap! You are probably WORLDs better than HER because you probably have a better personality! You are the prize! She should only be so LUCKY, read again, LUCKY, read it again, L-U-C-K-Y! to have you in her life!
That's the attitude you need to approach her with. And you need to believe it too. She's not some goddess. She's not something special. She's a girl and girls are a dime a dozen! You've really got to internalize this attitude because it's the only way you are EVER going to have a shot with her.
Then when you get that attitude down, you'll want to start treating her like it! Don't be afraid to buck her! Don't be afraid to make her mad at you. In fact, you WANT her to be mad at you, because that's what's going to build attraction to you. I don't advice you to be rude or ignorant or say something mean to her. I just suggest you be arrogant with her and treat her like she's something less than you.
An example would be you are going on a trip with her. I'd cut right in front of her in line at the restaraunt you go to as if it were nothing. When she says something, just turn around and say "Excuse me, do I know you?" with a straight face...hold it for a few seconds, then SMILE and turn around. She'll undoubtedly try again and then you say, playfully, "Jeez! What now? i'm tryin ta order hur!" (remember PLAYFULLY) and keep busting on her like that until she is "hooked".
YOU call the shots. YOU tell HER what she should THINK. You are the prize, and she is just a mere girl. She's an icky, dirty girl with cooties! lol Seriously, remember how you treated girls when you were a kid? Well that's how they want to be treated now. They want you to lead them, tell them what you are going to do, they want you to throw dirt on them, etc. She's no different now then she was then. NO DIFFERENT. So don't treat her different because she looks good!
And that, is a crash course in how to treat a girl you like. I'd really suggest ready more stuff here and I HIGHLY HIGHLY HIGHLY recommend you read the Book of Pook:
http://www.jbspencer.com/djb/Downloads/The Book of Pook.pdf