The iPhone Dev Team acted very fast to release the jailbreak for iOS 6.0.1 for the iPhone 4, iPhone 3GS and the iPod Touch. They released the tool to jailbreak iOS 6.0.1 on older devices; just one day after Apple released the new OS. However one thing to bear in mind is that this is the tethered solution, and not everyone will want to use it.
iOS 6.0.1 tethered jailbreak for older iPhone & iPod touch models released
Owners of the latest iPhone 5 and those with the 4S will have to wait for the jailbreak, however certain older devices can be jailbroken now. The process of jailbreaking iOS 6.0.1 is quite similar to that of the iOS 6 for the iPhone 4, 3GS and 4th generation of the iPod Touch.
Before you begin to jailbreak your device, you may wish to bear in mind that it will void the warranty on your handset. However usually you can un-break the handset if you should have to take it for service.
How to jailbreak (guide)
Backup the iPhone or iPod and upgrade to iOS 6.0.1 and that the computer is running the latest version of iTunes.
Download the ipsw of iOS 6 for your device
Download a recent version of Redsn0w. For the iOS 6.0.1 jailbreak, users need Redsn0w 0.9.15b1, Redsn0w 0.9.15b2 or Redsn0w 0.9.15b3
Users that need to download a new version should download Redsn0w 0.9.15b3 for Mac or Windows
Extract Redsn0w to the desktop
Open the redsn0w application
Ctrl Click on Mac (if on Mountain Lion) Right click and Run as Administrator on Windows
Connect the iPhone and click on Extras
Click on Custom IPSW and find the iOS 6 file downloaded in step 1
Click on the iPSW
After Redsn0w recognizes the file, click back
On the main screen, click on Jailbreak
Place the device into DFU mode, as shown in the video below and the on-screen instructions
Follow the on-screen instructions to jailbreak the iPhone 4 and install Cydia
Just boot to complete the iOS 6 jailbreak
In the future, to restart, connect the iPhone to the computer, open Redsn0w, click Extras and Just Boot.
You should now own a device that is jailbroken and Cydia should show on the home screen so that you can access app and tweaks. Hacking teams are working on the untethered jailbreak for iOS 6 for the iPhone 5 and the iPhone 4S.