The iPhone Dev Team along with many others have now released the Official iPhone 1.1.3 Jailbreak! I have just run through the process and its one of the easiest I have seen.
1. Download the Jailbreak Pack here.
2. Copy the files to the root of the iPhone/iPod Touch.
3. Set execute permissions.
4. Run install.sh.
A more in-depth guide is in the README of the Jailbreak pack. For those who want to see the process I have made a video of my first attempt at jailbreaking my phone. Sorry for the crappy video quality, I had to use an old webcam . Note: I have cut out points in the video where the installer appears to lag, when attempting the jailbreak process yourself it may take much longer.