Starting today you can jailbreak your iOS 6 and iOS 6.1 device with evasi0n. This includes the iPhone 5, the iPad mini as well as past generation iPhones and iPads. It’s an untethered jailbreak, so you won’t have to plug in your device each time you want to boot it up. Always nice, especially with a phone.
Here’s how to jailbreak your device. It’s a step-by-step guide provided by the evad3rs jailbreak team.
1) Back up your device by plugging it into your computer and choosing backup from the menu in iTunes.
2) If you have a jailbroken device, take note of all your installed packages, because the restore will remove your current jailbreak. If you’re not on a jailbroken device, don’t worry about this.
3) Restore and update to iOS 6.1 (the current version of iOS)
4) On the device itself, select “Set up as a new device” but in iTunes do not select anything yet.
5) Launch evasi0n (which you can download here.) and jailbreak your device according to the onscreen instructions. They should guide you through.
6) Open Cydia on your iOS device and it will “prepare the filesystem.”
7) Relaunch iTunes and choose “restore from backup) this will bring your App Store apps and music all back into your device.
8) That’s it.
Here are some FAQs, also provided by the jailbreak team: Link