How can I break the ice with her?

I want to say that you should ask her about some of the class work that ya'll had just gone over in class but if you don't really want to know that just makes you look weird. Honestly if she's the girl your talking about than I think you should just walk up to her.
But if you don't feel comfortable doing that then I would suggest eye contact. If she looks at you then smile and wave. If she waves back it's like opening a conversation.

Walk past her extremely close, but not to close that you touch her, just close enough that she notices you. Then if she looks at you smile and go introduce your self. This happened to me in high school this guy walked past as I was cleaning out my locker for summer and he walked kinda close. I was near the floor in my back pack so I thought that was rude of the guy with gray shoes, so I looked up and he looked back and smiled at me. I then stood up and he walked backwards and asked if I was gonna miss the place, we began a conversation from there.

The trick that always works for me (but for guys) is "accidentally" bump into her. It works best to have a friend push you into her, then you can say, I am sorry are you ok? My name is___" or you could just smile at her and if she is really friendly she might talk to you. I am shy so I probably wouldn't approach the girl. Or compliment her. But that usually doesn't start a good conversation, but it will show to her that you notice the time she puts into her appearance and you appreciate it.

Drop an ice cube by her while she's at he locker - then say, well that's one way to break the ice... if she laughs.. your in.. otherwise, move-on