This is extremely easy to do so idk if this should even be a tutorial.
[Win/Mac/Lnx] redsn0w BETA jailbreak (2G f/w 2.2.1) - iPod touch Fans forum
redsn0w.com

UPDATED TO BETA 0.3
"Apple Sucks" error message fixed, some "space" issues fixed. LogoMe now working for iPod touch 2G.
Full Changelog
Here.
A full restore back to the 2.2.1 firmware is recommended, but not needed for this to work correctly.
This tool by planetbeing & the iPhone-dev team does not contain a GUI, but you don't need any command prompt knowledge either. Just put into DFU and double click redsn0w.exe. NO LIBUSB NEEDED! This will modify the firmware directly on your iPod. No hassle of restoring! For firmware 2.2.1. This tool does not work with 3.0 betas. All MediaFire links courtesy of planetbeing's post.
A few users were not able to get the Windows version working. planetbeing has posted an update saying they have accidentally replaced the Windows binary with the Linux one. That has been corrected.
Download Here
Linux
Download Here
UPDATE: planetbeing has updated LogoMe for the 2G iPod touch. You MUST be jailbroken on the software above, (redsn0w 0.3) or it will not work. You can find it on Cydia. And remember, boot logos must be at most 480x320, be under 100 KB, and have at LEAST ONE (1) transparent pixel.
FadeThreeBlack edit: I already jailbroke my ipod touch before this better jailbreak came out, and i did not have to restore. This does NOT (NOT NOT NOT) erase the stuff on your ipod. Follow the directions in the .exe
The .exe is very self-explanatory, but make sure you're ready and time it right. Only really 1 manual thing to do.
Any questions? Post here!