Today, Apple released an update iOS 6.1.2 to fix exchange email problems alongside battery problems. The update did not patch the evasi0n jailbreak exploits nor the passcode bypass seen in iOS 6.1 and 6.1.1.
This Jailbreak Guide Works For All Devices (Excluding Apple TV 3) on iOS 6.1.2, 6.1 , 6.0.1, and 6.0
1. On your iDevice open settings > general > passcode lock and disable it until the jailbreak is done
2. Download and open evasi0n 1.4 found here: Download
3. Connect your device (Evasi0n should recognize it automatically).
4. Click “Jailbreak” and let the process begin.
5. Partway through, Evasi0n will notify you to tap a new icon on your device. Unlock the screen and find the new application called “Jailbreak”. Tap that and your jailbreak will continue.
6. Wait for evasion to finish, and your device will reboot, showing the evasi0n logo and varios status messages.
7. When your device reboots, Cydia will be installed and your device will be jailbroken!
Thats it! As with all untethered jailbreaks, there is no danger of rebooting your device, so there is no final step to boot tethered!