How-to Jailbreak iOS 6.1.2:
Step 1: Update your device to iOS 6.1.2 using iTunes (download iOS 6.1.2 from here): if you are jailbreaking your device, why not update it to the latest version of iOS? OTA updates might mess with the jailbreak, therefore a fresh restore via iTunes is strongly recommended.
Step 2: Turn off Passcode Lock in case you have it enabled. In order to do this, simply head on over to Settings > General > Passcode Lock > Off.
Step 3: Download Evasi0n 1.4, which adds the support for 6.1.2 [for Windows, Mac or Linux]
Step 4: Start up Evasi0n on your computer and simply click on the “Jailbreak” option. Kick back or grab a cup of coffee as Evasi0n does its work and jailbreaks your device. Remember not to touch anything while your device is being jailbroken.
Step 5: Once this is done, your device should boot straight back. You will see a new Jailbreak icon on your home screen. Tap on it in order to finish the process.
Step 6: Your device will now reboot quite a few times for a short while, before it boots into the jailbroken state. Once this is finally done, your device should boot back in a jailbroken state.
You are done: if everything has gone as expected, Evasi0n should indicate that the jailbreak is complete. Cydia should now also be on your home screen.