There are several sites where you can play chess online. My absolute favorite is freechess.org. It’s designed for serious players of all levels, from beginner to chess masters, without all of the distractions of more social sites (like Yahoo, for example). You can sign up for free (imagine that), and you can download free software that makes the experience a little easier. Once you sign up, you will be assigned a rating that increases or decreases as you win or lose. The rating allows you to compare yourself with other players and also helps you measure your progress.
It takes a little time to get used to their system, but after all, it’s free! Check it out, and if you see a player with the handle “mathtchr”, challenge him to a game!