Girls hate it when a guy asks, “What are you doing Friday night?” because the reason could be anything from being asked out, to being asked to cover a babysitting job so the boy could take someone else out, to being asked to volunteer for something.
@Tink1113‘s on the right track. Start talking about music, or movies, or something general, then ask her if she’d be interested in doing something with you some time. Then say, what about next weekend, and set the date from there. If there’s a dance or something at school that you’d like to go to, like homecoming, go ahead and ask her, and then work backwards from there on spending more time together.