She could have spotted you on a a friend's Wall, or a friend list, or even a Page/Group. Yet, your Facebook picture is the first thing a girl sees about your profile - it's the reason she'll click on your profile.
Therefore, to be desirable on Facebook, you need to have an attractive Facebook picture.
Using Your Facebook Album
You need to use your photos to look attractive - women usually gravitate to your photo album
immediately after clicking on your profile.
Make it a point to get in touch with people you meet at events and have them tag you if any pictures were taken - especially if women are present in these photos.
Even better - buy a good camera, or a good camera phone to carry around - even a trip to the mall becomes a photo-shoot.
Tagging your future girlfriend
A social occasion can introduce you to more people, all of which will usually Facebook. If you're tagged in an album, it's free publicity for you. More girls might want to check out your profile. Further, commenting on albums you're shared can serve as a prelim conversation with girls you find attractive (and vice versa)
Selecting Your Facebook Display Picture
If finding a girlfriend is an important aspect of your Facebook, use a picture that makes you look good. Not a random image of artwork, puppies, or emo posters. (And don't use Hrithik Roshan's picture!)
Ask your friends, especially female friends about photos which they like by putting them on your Wall. Take your best picture and make it your Facebook profile picture.
Changing Your Facebook Display Picture
If you have an active social life, you'll have a ready stock of different photos for your Facebook Display pic. If you don't, well, keep the following kinds of photos in mind while changing your pictures.
You: a traveller
In front of a monument, or at a beach, or even Disneyland. It shows that your world as a happy place.
You with girls
Pictures of you with pretty girls. According to the pre-selection theory, men who have beautiful women around them seem more attractive than a guy looking at a webcam.
You with friends
The simplest, most obvious way to show that you have a social life - pictures of it. On an average, a woman will find pictures of you with a happy, healthy smiling bunch of friends more attractive than your pictures of volunteering aid for poor people.