These days it is appropriate to ask someone for either their phone number or an email address since many people use email as their mail form of communication. Don't be shy! You have nothing to lose and everything to gain by asking someone for his/her contact information.
You may never see the person again and you don't want to have any regrets! Since part of getting out there is taking risks, it is important to push yourself a little bit beyond your comfort level. If you aren't comfortable asking for information, extend yours. A business card can be a great tool for this. As the conversation comes to its natural close, say "It was nice meeting you, I'd like to get together another time", while handing him/her your business card. "Give me a call sometime" is a great casual way to indicate you would love to see them again.
