The Users Guide for your iOS
http://manuals.info.apple.com/en_US/iPod_touch_2.2_User_Guide.pdf
says to purchase stuff.
1 Tap the price, then tap Buy Now.
If you were signed in to your iTunes Store account in iTunes the last time you synced
iPod touch, you don’t have to enter your account ID. Otherwise, you are prompted to
enter your account ID
Thus, it appears that with your iOS you have to sign iTunes into your account and then sync with iTunes on the computer to change the ID on the iPod.
You may also want to update to the last iOS for your iPod. That is a paid update that you get here:
Purchasing iOS 3.1 Software Update for iPod touch (1st generation)