What is the most logical next event?

How to get a girl to notice you
Become familiar to her.
Girls are more likely to talk to a guy if they are not complete strangers. Catch her eye in class and smile, nod at her in the school hallways, or make an effort to sit near her at lunch.
Of course, don't follow her around (that might creep her out) but simply making sure she knows your face will make her more receptive to talking to you at some point. Little things like asking her the date or hanging out at the same after-school spot will make her begin to start noticing you.