Well.. despite I usually like C1PH3R's replies this one would be the exception.
In my experience, you can have great success with girls you don't actually know, on FB.. Even if you don't have anything in common at all!
Just add the girl, if she accepts, just start a normal conv like you knew her already....
One of the top reasons people use social networks is because they're lonely and/or want to make new friends, and even if that is not the main reason for them to have a FB account (for example) They are accepting the fact that its really likely that some one will try to meet them.
FB pick-up obeys slightly different rules than real life (normal) pick-up. You don't need to be particularly interesting the moment you start chatting up, just have a cool Profile Pic, good conversational skills and the ability to be cool when she takes her time to reply to your chat msjs and starts asking questions
Being flirty over FB also obeys different rules (since there's no visual reference of your current body language). Depending on the text, the punctuation, the words you use and the timing, you might get the girl with ease.
For example
I see HB9, add her, IF she accepts, I wait 1 or 2 days, then start chat conv (in case she doesn't do it first) and just say Hi... how are ya, I think I know you but can't remember where, do you like hanging out at X place? Maybe i've seen you there, etc...
If questions like "where do I know you" "who are you" or stuff like that come up, i just answer straight.. I am John Doe, We dont know each other, I added you cuz I'm makin new friends

, I saw your profile tru some one else's (can't remember who)...
The idea is to be funny and to hook her fast. Do not show a Cocky and Funny frame too fast, or a good guy's.. It might not work, just be funny, be confident of yourself, and talk to her like you already know her..
About the timing.. Usually ppl use their FB during work hours (9am tru 5pm) so this might be a good time to hit up on casual conversation and gives you the advantage of an automatic False time constrain (my boss is here, wait, Im finishing up some reports, Im on my math class finishing my exam, Some one's knocking the door, wait, etc..)..... This is cool because FTC help you create the image, in her mind, that you are, either in charge of an important job at your work place, or at least you take charge of your own home.
If you decide to have a chat with her during evening hours (6pm tru 9pm), just consider the fact that those might be her Off work/school hours. The time she takes to contact her people, her friends, (both guys and girls) and she might not be too available for a stranger like you, so dont be surprised if she doesnt reply to your messages. Altough, on the other hand, if during evening hours she does reply and you manage to have a cool conv with her, you're on !!

That would be a good sign!
Now, late night hours (9pm tru 3 am) is usually (in my personal opinion) reserved for intimate chatt with real friends. Also, its very common that many girls turn off their computers early so.... Anyways, I'd recomend you the following..
Add the girl, if she accepts, take 1 or 2 days to start a conv. (preferrably during work hours or evening hours) Be funny, use false time constrains (gotta get some food, my boss is here, some one knocking the door etc), Do not be to strong on any Cocky and funny or nice guy attitude, BE it, but not too much. Do not try to impress her with stories, use media to create conversation topics (did you hear the news?, do you like this video?, have you seen my pictures? etc..)
When you've created enough attraction or interest (usually takes a couple of good, consistent FB chats, you can ask her out
I've had lots of success stories with FB girls that I get to meet in person later

FOR REAL, and in the past (before my 2.5 yeras relationship) I'd meet and date at least 1 FB girl every 15 days (well, maybe not that many

)

besides whatever girls i'd pick up in real life scenarios
Hope this works man.
BTW, about C1PH3R's post. Yeah. It's better if you get used to picking up in real life instead of FB..