Hi shorn9, it sounds like you really have the hots for this girl. Well, it's a good thing that you guys go to the same school, because you would be burning your chances a little bit by diving straight into the "what's your name, what's your number" deal... girls usually don't like that because, well, it's really overdone these days (especially if she's beautiful). I would suggest starting by making her notice you... next time you see her at school, give her a biig smile!
Next, a good way to "approach" someone at, let's say, at the library is to offer some coffee, or some water( "Hi..I've noticed you've been in here or a while, I was about to get myself some coffee, would you like a cup?") Afterwards, don't stick around and try to force small-talk.. otherwise, the gesture won't seem genuine. Next time you run into her, you can just say Hi.. compliment her on something, ask her what nationality she is (You're very pretty, what nationality are you?)... or, if you're feeling extra spicey, ask her if she'd like to grab lunch with you. If she says no, don't sweat it (or at least don't look like you are). If she says yes, you can go from there and strike a conversation about her interests, where she's from, and so forth. Remember to look her straight in the eyes when she's talking, and smile a lot!
Good luck!
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