Open iTunes. Now hold down Option (Mac)or Shift (Windows) key and click the Restore button.
Navigate to the Pwnage folder on your desktop and select the iOS 5.0.1 firmware ipsw. Click the Open button to continue.
iTunes will ask if you want to setup your iPhone as a new device or restore from the backup. Choose Restore from Backup if you want to preserve your contacts and other information.
Once iTunes has finished updating your iPhone to the desired firmware open the Pwnage folder on your desktop and launch the Absinthe application.
As prompted, connect your iPhone 4S to the computer via USB. Make sure to remove any passcodes or VPN settings you've previously set.
Absinthe will detect iPhone 4S. Click the Jailbreak button to begin
The application will take you through several steps of the jailbreak: Sending initial data, waiting for reboot, waiting for device to finish booting, Preparing jailbreak data, and Sending payload data.
You will be informed that the jailbreak is 'Almost done'.
On you device, locate the Absinthe icon and press it to complete your jailbreak. It could be on any homescreen.
If the server is down and you get an Error establishing a database connection message then tap the Settings icon on your springboard and turn on VPN.
You will get a configuration error; however, after about a minute your device will reboot with Cydia on the Springboard!
If you are still unable to succeed please be patient as the dev team's servers are under heavy load right now!
Run Cydia. Let it do all the necessary updates.
To have access to the root file system of your iPhone (via file managers like iFunBox or iPhone Explorer) install application called afc2add in Cydia.