The "random" approach has worked for me; I now have a woman!
I was hanging out with a friend from uni after class one day in april or may, and a female friend of his joined us. We had a few drinks hanging around on campus, then we went with the girl to her place which was nearby. Along the way my friend left us to go home as he was feeling ill, so it was just me and her in her house. We watched movies and chatted late. She invited me to share her bed but I declined and slept on the couch (being the gentleman I am). I thought she was really pretty and cool but I was a bit down at the time, and so was she, neither of us made a move. I was completely myself, feeling no pressure to pick her up.
I left in the morning, we hugged, and I felt absolutely retardedly spastic for not asking for her phone number. I thought I might see her again if I hung out with our mutual friend. He turned out to be good company, but after a few months there was still no sign of this girl.
Last weekend I noticed that a friend of my sister had added this girl on facebook, so I added her with a message asking if she remembered me from our chance encounter. She replied enthusiastically, we started chatting online and before I knew it we were on a date. We ended up at her place again, but this time I took the bed option.
She said she was glad I hadn't asked for her phonenumber that first time, as she was blue from a recent break-up.
I've been as weird as I can be and she thinks I'm a freak but also likes me. We saw each other again on the weekend and have plans to continue courting. And fucking.
So driftingblizzard, if a fucken wackjob like me can have success, so can you.