Your State of Jailbreak:
Good news! There are several jailbreaks available for your iPod touch 4G. Choose one of the options below and follow the tutorial to get yourself jailbroken:
JailbreakMe 3.0 is the easiest jailbreak ever. It’s a browser based jailbreak meaning that no computer is required. Just go to the site and install Cydia. Recommended
redsn0w is a very solid jailbreak that takes just a few minutes to complete and still is about as robust and full featured of a jailbreaking program that you can get. Using redsn0w 0.9.6rc13 you can get a fully untethered jailbreak which makes it an excellent choice.