Important Notes : Redsnow 0.9.12b1 support all Apple devices except Apple TV. You should to have iOS 5.1.1 Firmware before using this jailbreak.
How To Use Redsnow 0.9.12 b1 To Jailbreak iOS 5.1.1 :
STEP 1: Download Redsn0w 0.9.12b1 for [ Windows ].
Dwonload Redsn0w 0.9.12 b1 for [ Mac ]
Download iOS 5.1.1 IPSW Firmware
STEP 2: Now connect your iPhone to the computer and run Redsn0w.
STEP 3: Click jailbreak, and wait patiently until the device restores, then resprings, and the Cydia logo appears on your Home screen.
STEP 4: Now you are done. You can open Cydia now and install it on you device.
I advise you to watch the following video. This video will guide you and show how easily you can jailbreak iOS 5.1.1 untethered using Redsn0w 0.9.12 b1 for both Windows & Mac.
Watch the Video :