Asking a classmate out?

Since it's a writing class...write her a cute note! You know, like you did in elementary school!
"Hey (name here), I'm (your name) and I think you're pretty neat...do you want to hang out sometime? Y( ) N ( )"
Chances are she'll smile and accept.

Did you say writing class? Write her then, ask her if she likes to watch a sport game, or going to the new movie(choose one you like:p) anything...and then after she answers ask her if she would like to go out with you to see the movie or watch the game.

The first thing would be to say hi and start a casual conversation - if that goes well for a few days or more - then just ask her out.