Here's what you do: whip it out, take her hand, and tell her that you're going to take her on a little exploration. If she doesn't slap you, then you're in.
Just kidding about that man. You don't really need to come up with anything to talk about with her. If you guys get along really well and are into each other, that will just come naturally. There shouldn't really be any awkward silence. And just do whatever you want with her. If there's a movie you both want to see, then go see it. Go out to dinner, but don't pay for it all yourself, that will give you away. Just hang out a few times, even if you just watch tv together. That way you are just getting to know each other better and are getting a good feel for one another. Then if you still want to start a relationship with her, tell her how you feel, or just plant one on her. Your choice. Or hey, maybe she'll take that step first, which will make things easy for you. Bottom line is, just take it slow, and don't sweat what to talk about or any of that garbage. Just be you and see what happens. Good luck