Before you attempt to jailbreak your shiny iPod touch 2G, be aware of the caveats and potential device hazards. As the README quite explicitly states, this exploit is unsupported and requires tethering the device to your computer to jailbreak. What this means is that unless you are perfectly comfortable with using buggy development tools, installing some extra libraries and interacting in DFU mode, you really shouldn't be attempting to jailbreak your device.
It looks like you need to replace some special files in PwnageTool 2.5, create a custom ipsw for 2.2.1, extract and rename some core files and then connect to your device via DFU mode to patch and replace those files. That's a bit of an oversimplification, but the gist is: this is more complicated than just running one program.
I looked at doing this on my own 32 GB iPod touch, but I think I'll hold off. First, it isn't clear that the DFU issues the Dev Team is reporting for the iPhone jailbreak/unlock with OS X 10.5.6 don't affect redsn0w. Secondly, I'm not convinced that anything available via jailbreak is worth risking my $400 investment. Alternate iPhone themes look really cool, but a working iPod touch is even cooler. Thirdly, I really don't want to play guinea-pig to something that isn't ready for mainstream release.
I'm passing on the iPod touch 2G jailbreak for now. So iPod touch 2G owners, what say you? Are you going to take the plunge or are you going to watch from the Lido deck with me?