I've seen people bake cupcakes with a piece of paper wrapped in tinfoil baked inside asking people to homecoming, or you could leave her notes in her locker every day for a week anonymously complimenting her and after a few days to a week of that, tell her your name on one of your notes and ask her. Buy her flowers and maybe take her somewhere pretty to ask her. Or get her parents in on it and ask if you can write on their driveway in chalk asking her. Or you could always use the "I know this is cheesy, but will you go with me to Homecoming?" tactic written on a box of pizza.
