How do I ask this girl out/get to know her through Facebook?

[Tom P]

You are on her friends list, so you can send her a private message. You don't have to make a public statement of your interest in getting to know her. In the message just ask if she would be interested in meeting some time. She says yes, you arrange a short meet, she says no, you move on and leave her alone. If she indicates that she is unavailable, and you'd like to be friends, say so. If you aren't interested in being friends, say so, move on, and leave her alone. If she is not interested in being friends, move on, and leave her alone. Good luck.