Start small, kid. Offer to buy her a coffee and whatever they have in the dining area that looks like a pastry, and just sit and talk. If they have a viewing room, perhaps they might have something like a movie you could watch together. Don't get all formal until you're sure you won't panic and ruin things. :)
JJ needs more votes. If you have a few to spare, click on this link, and leave them one at a time--those of us who love this comic will thank you. ^^
Nope. For as much as he and Clara hang out, this is the first time he's officially asking her out on a date. This tidbit will actually be brought up later.