Note: If you are using Installer on 1.02 currently, install MobileFinder (Installable from Installer App) and delete /var/root/Library/Installer before updating to 1.1.1 to save some headaches later on.
1) Go into iTunes and Sync your iPhone to your PC to create a fresh backup of all your contacts, settings, etc.
2) Go into preferences and then the iPhone tab to make sure you have a backup of your iPhone listed.
3) Go to the Firmware Download Page and download 1.1.1 to your computer.
4) Then connect phone to dock, have ITunes running, and hold down home button and power button for about 10 seconds or until the screen goes black.
5) Now release the power button but continue holding the home button. After about 10 seconds the computer will detect the iPhone in restore mode, and iTunes should tell that the phone needs to be restored.
6) Hold down SHIFT key (Windows) or Option/ALT-key (Mac) when clicking the Restore button, and select the file you downloaded in step 1.
7) Let the restore complete and ignore the error at the end, if any. (Should be error 1013).
8) Click Download and Update. This process will take several minutes.
9) After the update is done, continue to jailbreak and unlock it.
10) After completing the Jailbreak and Activation step, iTunes should now ask you to restore that old backup. Make sure you hit Yes.