How would I go about becoming friends with a girl that is not in my class? I am out of ideas and I don't want it to come off creepy because she doesn't know me.

Put "conversation starters" in the search bar.  You'll come up with site after site filled with ideas.

For example if you're in the cafeteria, "That looks good.  Have you tried it before?"  Or if your cafeteria is notorious for crummy food, "What's the best of the worst here today?"

How old are you?  Just go up to her and introduce yourself.  Obviously, you're in the same school .. So you have that in common.