Well, I started playing guitar when I began typing faster and faster. I don't really know how to play the guitar but I simply put my hands on the home row keys, and started typing. Now I type like crazy fast.
Practice, practice, practice. I wouldn't consider myself as a fast typer, but I can definitely type more than slow without looking at my keyboard. Try spending like an hour each day practice typing up a story or something. Also, you can improve your typing by chatting with your friends on social networks or games that let you type to talk to other people.