iOS 6.1.2 can be jailbroken fully untethered using evasi0n. All iOS devices running iOS 6.0 through 6.1.2 are supported, including iPhone 5. While jailbreaking generally does not cause any harm to your device, we strongly recommend you to back up before you proceed further. Also if jailbreaking is illegal in your jurisdiction, then please exit now. Follow the following quick steps to get going:
1. Make sure you are running iOS 6.1.2 (Does not support 6.1.3)
2. Turn the Passcode Lock off. (Goto Settings >> General >> Passcode Lock >> Off)
4. Start evasi0n on your computer and click on the “Jailbreak” option. Do not touch anything while your device is being jailbroken.
5. Once 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.
6. Your device will reboot quite a few times for a short while, before it boots into the jailbroken state.
If everything has gone as expected, evasi0n should indicate that the jailbreak is complete. Cydia should now also be on your home screen.