Working as a cashier gave me some good opportunities to chat with coworkers. Meetup.com and Couchsurfing.org can also provide some great chances to chat with people.
Before going out, check Google News and Fark.com for any amazing or funny news stories. Ask the girl if she heard about this or that entertaining news story, and if she has, discuss it; if she hasn't, explain it to her.
Ask them how their week/weekend went. Do they have any plans? Express a genuine interest in them. Try to ask them things you think they'd enjoy talking about. What's their dream job, any places they've always wanted to visit, do they have any summer vacation plans, etc. Find common ground and shared interests between the two of you.
Try to stay away from questions with simple yes or no answers. Ask open ended questions. Instead of asking "Do you like x," ask "What are your thoughts on x?" Practice active listening. For example, if she mentions she's always loved architecture, then that's your cue to ask her what about it she finds so appealing.
Good conversation is more of an art than a science. Just get out there and talk to people. Some of your conversations might stumble initially, but that's no big deal. You'll get more comfortable and naturally free-flowing with it as you go along.