Compliment her lightly the week before you ask her, do favors for her, little to bigger, then lastly, ask her during a casual conversation if you two should go out for a bite or movie or walk. Try to find out what she likes to do and if you like it too, see if she's available to go out with you and do it. Good luck!
1st of all be yourself, go up to her introduce yourself don't say/do anything you wouldn't regularly do. If she likes you then you got yourself a date if not then it wasn't meant to be but don't beat yourself up over it. Its better to ask and get an answer than to stay quiet and live without knowing.
Asking a girl out is an invitation to go do something. Do NOT ask a girl to "hang out"; that will only make her dad furious. (I'm a dad. Think about it.). Do NOT ask her to be your GF or to go steady -- that's like buying a car without taking a test drive. Invite her to go do something on a specific day & time: like to go to the ball game next Friday, or go have a snack after school. **** The reason to avoid the "hang out" date: girls have to tell their parents where they're going, what they're doing, etc. if MY daughter ever told me a boy asked her to "hang out", he'd be dead meat. Get it? I hope so.