You can start using the Facebook applications to indirectly connect with her
. There are applications to send drinks, hugs, gifts and all sorts of things. Start writing on people's walls or use the Flirtable application. This will break the ice between you and the woman of interest and help her gradually have some sense of trust and comfort in conversing with you. From there you can then proceed to sending her private messages to get to know her on a more personal basis. Shortly after you can then suggest meeting up for dinner or some other date idea.