I want to recommend a series of posts by Warren "Mook" Wilson, author of How to Be A GURPS GM.
Warren has been doing a series of posts to introduce GURPS and walk through the mechanics of play.
The first post, Welcome to GURPS, has links to the rest of the series at the bottom.
It's an excellent walkthrough of the system and how it works and how it plays. Not only that, it's exactly the kind of stuff I think should be written but I never actually get the enthusiasm to sit down and write. I'm happy The Mook did this and I wanted to highlight it here - especially so I can point new players to it whenever I encounter them.