I generally accredit my ability to type on a computer to those days on ICQ during highschool.
A better, more structured, approach would be something like this online typing tutor. TypeOnline.co.uk is a simple site that offers a series of lessons for keyboard accuracy, speed and other related exercises.
Even if you just want to check your Words Per Minute, this is a simple and accessible place to get those fingers waggling.
Learn To Type Online - [TypeOnline]