First off, don't just spontaneously friend request some girl from your Facebook network and really don't just go randomly friending people on MySpace, you outdated pervert. The only way you can non-creepily get a girl through free, non-Match.com, online pursuits is if you have previously met her in person--met and spoken to her in person. Seriously, stop being so creepy.
Ok, so you met your girl, but, for whatever reason, you didn't actually get her then. All is not lost. 2-3 days--depending on how much you spoke--after your first meeting, you friend request your girl with a personal message that includes some reference to your previous conversation (i.e. "Did you ever figure out how to solve that math problem?" [If you're an effing loser.] Or, "The name of the guy who played the body of Darth Vader in the original Star Wars trilogy is David Prowse, in case you were still wondering." [If you're awesome.])
Assuming she accepts your virtual friendship, she will be obliged to respond to your message, thus opening up the lines of beautiful communication.
She'll reply with something cute and flirty like, "Bob Anderson was in the suit for the lightsaber fighting parts though. I can Wikipedia things too ;)" [Guys find intricate Star Wars trivia cute, right? Right?] And then you guys flirt-message back and forth a few times until, on a Friday--not like a Tuesday--you end your message with, "What are you up to this weekend?" When she tells you what she's doing and asks what you're doing you say, "I was thinking of seeing/going to Be Kind Rewind/the zoo/that party too!" (The exclamation point is up to you.) Then, if you've done everything correctly and avoided being creepy, she'll probably say, "Maybe I'll see you there."
Don't respond to that message. Log offline, go run into her at the movie/sporting event/religious demonstration/whatever, and seal the deal.
Now, what was the coolness verdict on Star Wars trivia?