How to talk to her

I'm in highschool and there is this girl I like and I think she might like me too. We don't know each other too well and i was looking for suggestions on how to talk to her and get to know her and kind of hint that I like her without being creepy. Its not like I can ask her to the movies or something since we dont know each other too well and that would be kind of weird just to ask out of the blue like that. My problem isnt that I'm shy, but I don't know what to say. I thought maybe I could start to initiate conversation slowly by like asking her what the homework is or something but I don't know where to go from there.