Jailbreaking your iPod Touch/ iPhone is the most simplest on 1.1.1.
All you need to do is navigate to http://www.jailbreakme.com in Safari on your iPod Touch/ iPhone and click install AppSnapp. Then Safari should crash but just leave your iPod Touch/ iPhone until it reboots.
Then you will see a new application called Installer where you can get 3rd-Party applications.
Congratulations, you now have a jailbroken 1.1.1 iPod Touch/ iPhone.