Jailbreak iOS 6.1.1 Untethered Using Redsn0w / Evasi0n

What you will need:

• Redsn0w 0.9.15b3 [Windows / Mac]
• An iPhone 4, 3GS or iPod touch 4 running iOS 6.1.1 beta 1. (from iOS Dev Center)
• iFile, the jailbreak file exploring tool which can be downloaded via Cydia.
• The original iOS 6.0 IPSW for your device. 

How-to jailbreak iOS 6.1.1 tethered:
Step 1: Connect your A4-powered iOS device to your computer.
Step 2: Open Redsn0w, point it to the iOS 6.0 IPSW by going to ‘Extras’ and then selecting ‘Select IPSW’, and then hit ‘Jailbreak’ from the main window.
Step 3: Once the process is complete, select the iOS 6.0 IPSW once more, and select ‘Just Boot’. Your iOS device is now jailbroken tethered and booted up on iOS 6.1.1 beta 1.
How-to jailbreak iOS 6.1.1 untethered:
Step 4: If you haven’t already, install OpenSSH and iFile from Cydia, and navigate to System/Library/CoreServices.
Step 5: Scroll down to the bottom, tap on SystemVersion.plist, and open with text viewer.
Step 6: In the .plist, look at the information at the bottom of the page in between the tags. It should say ’6.1.1′. You’ll want to tap the Edit button in the top left-hand corner, and change that string to ’6.1′. Then, click Save, located in the top right-hand corner.
Step 7: Navigate to Cydia, locate evasi0n 6.0-6.1 Untether, and install it. After a reboot, you’ll be untethered on iOS 6.1.1 beta 1. Alternatively, you can also install the untether manually using Evasi0n’s .deb file in iFile. Once you’re all done, repeat steps 4 through 6 and change the version number back to 6.1.1 from 6.1.