How to jailbreak iPod Touch 3.1.3 with MAC OS X

First, degrade you iPod to 3.1.2 because 3.1.3 is not well-supported by iPhone's hackers' community.
For iPod 2G, you need "iPod2,1_3.1.2_7D11_Restore.ipsw"
It can be downloaded by searching the file name.

Then follow the steps here
http://tysiphonehelp.com/?p=482

Very simple and I just tried, it works