I'm a complete beginner; my first game of Go was in August '05. I was drawn to Go by my amateur interest in computer AI, game theory, and the related research regarding this game.
For an introduction to the game, I picked up The Book of Go (Cobb) at a bookstore. I am now reading Go for Beginners (Iwamoto) and practicing against GnuGo and against other beginners on LittleGolem.net (on the 9x9 board in every case). I save all my games and study the interesting ones. My short term goal is to reach the next kyu rank; my long-term goal is to be able to decisively outplay the strongest computer Go program. Supposedly that should take less than a year-- we'll see. ;)