New guy in love with new girl

This year my family changed our living place. We now live in a big city, and I go to a big school. My class is quite big, everyone is friendly, but there's one girl I'm very attracted to. I have no previous experience in relationships, so I have no idea what to do. Coming up to her and start talking to her (Hi I like your shirt, it matches your eyes, wanna hang out?) or me, or weather, (or anything, really) seems silly to me, even if that "shows my confidence in approaching her with nothing to talk about" according to wiki-how.
I saw her glancing at my direction several times during our lessons together, but I don't know if she was looking at me, someone besides me, or just to know what's going on in class. I also saw a tip online about trying to sit next to her or getting to work on the same project, but I can't think of any way to do so. I do, however sit behind her in one of our lessons.
I don't know if we have anything in common to talk about, so I think I should just wait and find out what she likes (which is hard without talking to her :upset:). But even if I do find out, coming up to her and asking her about something I know she likes will make her suspicious, she might even think I'm some sort of stalker :tough:. So, I'm asking, what should I do? I want to be friends with this girl, someday maybe even start dating :goofy: , but as you know, I have no idea where to start.

Info about me:
16 years old
186 cm tall
Rather good looking
Not really funny

My English is not perfect, so there may be some mistakes. Sorry :/
Also, if this is not the right place to post, please redirect me to where this post should be.