iOS 5.1.1 unteathered jailbreak
Download Redsn0w 0.9.12b1 for Mac
iOS 6 unteathered jailbreak
1. Open the application, if you are on Windows Run as Administrator.
2. Select your device and its firmware from the list.
3. After that select the version to which you want to upgrade your device.
4. Now press the make it ra1n button. It will take sometime to perform the job.
5. Once it finish, reboot your device. You are done!