Yes. You casually introduce yourself, mention a thing or two in common (same groups for instance), and ask if they'd be interested in getting to know each other —assuming you have a solid FB profile and not something fake. Pretty much like you'd walk up to a person in a real life in a social setting and say Hi. Many of my friends met their girlfriends like that. If you don't get a reply then that's your answer, no hard feelings. If they're a friend of a friend, well, you just ask your friend for an introduction. I don't know how things are in the US, but it's not considered awkward at all in my country. I've had women approach me in this same way as well.