i do this a lot actually, with much success.
i add the girl. if she accepts the friend request then it's on. i message her and say:
"Hey have we met? you looked familiar so i added you =p" (copied that verbatim from the inbox)
they reply usually with something like "no i don't think so"
then i neg a little with "ahh, maybe i'm just going crazy..or maybe you are. who knowss

"
they usually respond well to that. from there i just chat them up. flirty, of course.
note that I'm in high school. if you aren't then the attitudes and social behaviors of the girls may be different. also, all the girls i do this to i have 20-100 mutual friends with on facebook. Good luck!