"Would you be interested in a relationship?"
"Be my girlfriend?"
"Could we be more than just friends?"
Which one? Or a different one entirely? Might as well just get it over with and suffer the heartache. Or.. you never know
Out of the blue? None of those. Girls are peskier, more elusive animals.
Start with conversations. Keep one going, and have them regularly. Find out what both of you are interested in. If you find yourself talking to a wall, she isn't interested. If you find that you're starting all of the conversations, you haven't hooked her yet. Give some hints, at least, before you ask, so she has an idea that you might and maybe an answer ready for you.
If she's told you she's not looking for a relationship, ask if she would want to try something casual. If she's told you that she's still not sure about how she feels about an ex, try accepting that and waiting a few days; time to think has changed many minds. If she's never been in a relationship, word it more subtly. Tailor it to the girl; some girls like to talk quietly and casually, some want a romantic setting, and some just want the right person. If you're afraid of asking, you could hint at the prospect and see how she responds. If you've ever researched body language, there's a good chance you'll know hew answer before you ask.
If she says no, I wouldn't get too hung up on it. If she says yes, remember that communication is key.
I mean, you'll have to kiss her first. I hope you know that.
You're going to have to kiss her once, say something clever, and then pull her in for another kiss. After then you'll say, "Be my girlfriend." No asking, no inflection at the end that makes it seem like a question. If she says no, shrug it off with something like, "Okay, your loss" and move on.