1

Download the Redsn0w file from the iPhone dev website and the 3.1.3 firmware from Apple, listed in the Resources section below, then unzip the Redsn0w file with the ZIP file reader.
2

Double-click the Redsn0w icon in the folder you extracted to. Connect your iPod Touch to your PC via USB cable.
3

Click "Browse" in the window that appears, then double-click the firmware you downloaded.
4

Click the "install Cydia" option and click "next". Press and hold the power button on your iPod Touch, then slide the button on-screen to turn it off. Click "Next" on Redsn0w.
5

Press the power button on the iPod Touch and hold it for two seconds, then press and hold the home button for 10 seconds while still holding the power button. Then release the power button and keep pressing the home button on your iPod for 30 seconds. Click "Finish" when Redsn0w indicates the jailbreak is complete.