After you engage them in conversation, just tell them you'd like to talk to them again - in just those terms. "I want to talk to you again. What's your number?" or "How do I reach you again?"
I've always felt that pulling out a cell phone and punching in the digits cheapens the mood. Fortunately, my work requires me to keep a pen and paper handy.
Then part ways as if you were on your way.
If it's someone you have repeated contact with, be patient with it. Wait for the...