Whatever you do, just don't "whip it out." (Sorry...a little J&SB humor)
Seriously, you kids have it so easy these days. Cellphones, text messaging, e-mail and instant messaging have made this so much easier. Back in my day *in old man voice* we had to talk to girls face to face...or worse, call them, at home and face having to speak to an unsympathetic sibling or *gulp* a father!
She has a friend, you have a friend. See if everyone wants to go get some lunch. Make sure your friend knows he's "mighty wingman". It will be a little more relaxed and y'all will be able to get to know each other without the awkwardness of staring at each other over the table, in silence, trying to think of something to say.
After this, you will be able to say, "do you think you and I could go out sometime?"
"Purgatory's kind of like the in-betweeny one. You weren't really shit, but you weren't all that great either. Like Tottenham."
I'll try being nicer...if you'll try being smarter.