It's very easy to get confused about all of this
Everyone has his or her own idea of how you should proceed and what you should say.
Personally I don't like to make a big deal out of it. My favorite is to invite a girl out for something casual, like a cup of coffee. Relax and talk about whatever pops up. It doesn't really matter what you're talking about, you can talk about almost anything really.
Basically, just relax.
You'll be alright.
edit:
In your situation I would start by talking to her about some neutral thing (an article, a movie you just saw, phone bills, whatever) then after talking for a bit ask if she wants to join for for a cup of coffee, or arrange a meeting sometime later. Bingo, you asked a girl out - pretty casual and it wasn't that difficult.
After your "date" and everything you can ask if she wants to go see a movie, or a theater play, or something else. Go do things that you want to do and ask her to come with you because you like her company.
Be yourself at your best - don't be afraid of throwing some jokes out there and playing with her. You're out to have some fun and it's not a job interview. Just make sure you're comfortable and making her comfortable. If you feel that things are going the wrong way then just back up a little.