Instructions
Although there are many ways to jailbreak an iPod touch/iPhone, I have found that this way works best.
Step 1. Download the 3.1.2 firmware from the "files" section. Make sure that it is 3.1.2, not 3.1.3.
Step 2. Download blackra1n, also from "files".
Step 3. Connect your device, then open iTunes. Sync your device and backup all files. Press and hold shift, then click restore. Navigate to the firmware file, and press OK.
Step 4. Once the restore is finished, load all of your files onto your device.
Step 5. Run the blackra1n file, and click "make it ra1n".
Step 6. Once the program is finished and your device reboots, run the blackra1n app and install either Cydia or Rock. I recommend Rock because it is faster. The blackra1n app can be deleted after you install Cydia or Rock.
Congratulations! You now have a jailbroken device.