A tethered jailbreak means you will need to connect your device to the computer each time you reboot.
Create a folder on your desktop called Pwnage
Download the latest version of RedSn0w from here and place it in the Pwnage folder. Likewise, download the 6.0 firmware from here and place it in the Pwnage folder. (Note: you do not need to download the 6.0 firmware if you are already on iOS 6.0)
Extract the RedSn0w zip file by double clicking it.
If you haven't already updated to iOS 6 then open iTunes from your dock.
Select your iPod from the list of devices on the left. Now hold down Option and click the Restore button. Restore is preferred as it won't create any wasted space on your iPod.
Navigate to the Pwnage folder on your desktop and select the 6.0 firmware ipsw. Click the Choose button to continue.
iTunes will now update your iPod to the new firmware.
Right click or control-click the redsn0w application from the redsn0w folder we extracted earlier and choose Open from the popup menu that appears.
Once RedSn0w opens ensure your device is connected and click the Jailbreak button
Turn OFF your device then click the Next button
RedSn0w will now guide you through the steps to get into DFU mode. You can find more help with DFU mode here.
Hold down both the Home button and the Power button for 10 seconds.
Release the Power button and continue holding the Home button until RedSn0w detects the device.
Your iPod will now be exploited with limera1n.
RedSn0w will now prepare the jailbreak data.
Select Cydia from the list of options and click Next.
Your iPod will now be rebooted again and RedSn0w will begin uploading the new RAM Disk and Kernel.
Once this is complete you will be notified that RedSn0w is done and that this is a tethered jailbreak.
Once you have jailbroken you will need to rerun redsn0w to boot tethered.
From the main RedSn0w menu click the Extras button.
Select Just boot from the Extras menu to boot tethered and follow the instructions to put your device into DFU mode again for boot.
*A big thanks is owed to the iPhone Dev-Team and Geohot for their hard work and contribution to the iPhone community.
If you need help with this tutorial please post a question in the comments or submit a question to the iClarified community using our Answers section.