I always tell myself everyday that I'll go over and talk to her, but never do because I think she's way out my league.

OK lets start with there is no girl out of your league for one. Everyone is on the same field you just might not have the skill to hit the home run yet. What you have on your side is that Men are driven primarily by looks and women are driven by persona then confidence then a toss up between looks and personality. When I say persona its how you come across and if you come across confident you are ahead of the curve but the longer you wait to go talk to her the more unconfident you become in her ideal of your persona. The first time she saw you she must have saw confidence in you maybe you entered the room having a great day and just smiling laughing being happy. Some may say this does not matter but my friends own a company where they study this and get paid to show the average guy how to get that girl. What you need to do is stop sitting back thinking about what to say. You walk up to her say Hi my name is Mike even if you know her name you ask her for her name so any lose in confidence she has had in you maybe lost because she will think you have not really thought about her till now and you didn't hesitate. Or you can go the latter and walk up to her say you have noticed her and were to shy and you know her name see how far that gets you normally not far because it shows lack of confidence. You need to go talk to her talk to her like she is a friend of yours joke around don't stay there too long you won't be interesting that long. Get her number! Hand her your phone tell her to give you your number you will call her later. Here is the key to 99% of the time getting the girls number hand her the phone and stop paying attention to the phone even just turn around talk to someone else show her you know she wants to call you. Take your phone when she is done and walk away don't doddle. Text her 15 mins after she is no where near here that is was a pleasure to meet her and that you are mike. Don't explain where you met show your confident that she will remember. Do not text her again till she texts you. She will text you.

Yeah I can understand why this might be kinda of hard because it's not like you really talk and stuff. If you think she is really cute, that might be a good reason. But do you know anything about her personality or interests? Because if you thought she was really nice or interesting, that might motivate you to at least say hi.
Try to think of something you could ask about that you both have in common. Like asking if she has ever taken a certain class or had a certain teacher or about an assignment. Then you can say thanks and at least tell her your name and say you'll see her around. After that, you can keep chatting with her about school-related things. I think that would be the easiest way to start.
If she keeps staring at you, there must be some reason. Don't convince yourself she's out of your league until you've at least tried saying SOMETHING to her. She might not feel that way at all. I had a guy friend tell me he thought I wouldn't like some of his friends because they were too geeky, but I actually love geeks! So give it a shot :)

I used to think like that too, then one day I said to heck with it and just talked to him/guys. Just go up there and say hi, and see where it goes from there.

Ok, you have to view dating as a game, because well that's what is, you have strong players, and weak players, at this point your are one of the weak players. Everyday that you sit back and don't talk to this girl is giving more guys the chance to take her right out from under your nose. And your reaction will be something like this, dang I really wanted to get to know her better and now she's with that jack ass what the hell. If you keep this up, you will constantly sit back and watch other guys get all the girls you like time and time again.

So far this girl is possibly showing an indication that she likes you, and your doing nothing about it. Chances are she won't come over to you, she probably won't even start a conversation with you. So if you really want her then you gotta go out there and get her. If I was sitting down and some girl was staring at me every day, I would stare at her back and smile of course and once she looked away, I would get up and go over to her and say, I won the staring contest, do I get a prize, then say no no I am only kidding about the prize, I haven't even told you what I wanted yet, oh by the way my name is so and so and you are...

So now you got her name, I don't know why but women love it when they hear their name over and over again in a conversation. So you have to have some sort of conversation to start with, don't ask her anything that is obvious like what school do you go to, how many bros or sis do you have, and blah blah blah, those are lame and she will get bored and probably say something like I really have to get going. Think of somethings that she can respond to that aren't yes and no answers, and also don't talk about video games or school those are boreing to women. Be creative think of something good.

If you have something good going like she's actually responding say oh dang hey sorry I gotta print some stuff out before class, but it was nice meeting you and you know what I tell you what lets finish this conversation over dinner friday, that is if your boyfriend doesn't mind me taking you out to dinner. I use that line all the time it works like a charm. Your going to find out right then and there if she has a boyfriend because if she does, well your waisting your time, and if she doesn't there you go you got a date.

Then say let me get your number, or better yet let me type it in your phone, when you type it in call your phone and say ok cool now I got yours. OR if she says no let me just have your number give her your number and then say call me right now so I know I have yours. Then say well I'll give you a call soon, maybe tonight but I don't know I got some stuff to do, so if I don't talk to you tonight then I will see you tommarow

I would be careful. Women are weird and you can never tell if one likes you. Just because a girl looks at you and says hi to you doesn't mean she likes you!