I am using a recently updated iPhone 4s 5.1.1 and this is how I jailbroke it using Absinthe on Windows 7.
Prerequisites
This is fairly simple
- Install iTunes
- Make sure your iPhone is updated to 5.1.1
- Run Absinthe (it will extract itself into a new folder in the same directory)
- Run the new Absinthe
- Select Jailbreak
- Wait a couple of minutes for the program to finish its work (The iPhone will restart, be patient)
That is it, your iPhone reboots with cydia installed