Let’s jump on how to Jailbreak iOS 6.x with Evasi0n::
Step 1: First off, make sure you’ve backed up all data on your iPhone. You can connect your iPhone to iTunes and backup the data (or use iCloud, optionally). This is an important step because, although the jailbreak is expected to go very smoothly, there’s no harm in taking the necessary precaution.
Step 2: Now, open the Evasi0n jailbreak tool.
Step 3: Connect your iPhone/iPad/iPod Touch to your computer via the USB connector.
Step 4: Evasi0n will now detect your device. Once it has identified it, click Jailbreak.
Step 5: As the jailbreak proceeds, make sure no other software tries to access the iPhone (iTunes, iPhoto etc.)
Step 6: After a while, you will be asked to unlock your iPhone (slide to unlock) and press on a “Jailbreak” icon (it is the new evad3rs icon).
Step 7: Once you’re done with this, your iPhone will reboot a few times. There’s no need to panic as the jailbreak gets over.
Step 8: Check to see if the ‘Cydia’ icon is on your springboard. If yes, congratulations! You just jailbroke your iDevice!
That’s it! Your device is now completely jailbroken (untethered). This means you can reboot your iPhone without having to do the DFU-mode thing ever again.
This jailbreak works with:
iOS 6.1, 6.0.2, 6.0.1, 6.0. Older firmwares are not supported.
Supported devices number up to 22 (and these include all iPhones and iPads and even iPod Touch). Apple TV 3 isn’t supported but older versions are.
Below is a video tutorial that will walk you through jailbreaking process: