Don't hesitate, be calm, smile, look into her eyes. Mention that you were thinking of doing X, ask her if she'd like to go out on a date. Whatever you invite her along to do shouldn't be intimidating, movies are perfect, getting lunch somewhere is also nice. Avoid school functions or coffee or anything where it will be difficult to have fun, avoid dance clubs or concerts or anywhere it will be difficult to talk. If your school has intramural activities like biking or boating that's another option. It shouldn't be anything that might embarass her or isolate her alone with you. If she says yes, smile a little broader and set a time, get her phone number. If she says no, shrug and say "Maybe some other time.."

Keep things simple, elaborate bizzare schemes to get a girl to go out with you only work in disney kid's shows.