In this post I will be giving you a full guide on How to Jailbreak ALL DEVICES on iOS 6.1, which include the iPhone 5 and iPad Mini. Unfortunatly this will not Jailbreak the AppleTV 3. The video above will give you a full guide on how to follow the steps to complete the Jailbreak sucessfully. All the download links and details will be inside the post.
UPDATE: Evasi0n now also Jailbreaks iOS 6.1.1 on the iPhone 4S, I would suggest updating to 6.1.1 before Jailbreaking.