You use your ring finger for the A, your middle finger for the S and W (leave it rested on the W), and your index finger for the D, and your thumb rests on the space.
Man, I was doing it all wrong all this time. No wonder it was uncomfortable! No one ever told me how!
You must not have played computer games back when the arrow keys were used by the right hand? It's the same layout and a pretty natural transition to using WASD on the left hand from there. I do know a guy who wasn't willing to ditch the arrow keys though, so now he just slides his keyboard way to the left and uses arrow keys plus the various buttons in that area: right shift/ctrl, numeric keypad, and the ins/del cluster for all his other commands.
Sounds like a royal pain having to rebind your keys for every single game you play.