Q: I have an 8 GB ipod, with IOS 2.2.1.  How do I download 2.2.1 compatible games for my ipod?  Thanks!

You have a 1G. You can update to iOS 3.`1.3

Connect the iPod to your computer and update via iTunes as far as your iPod model allows

iOS: How to update your iPhone, iPad, or iPod touch

A 1G iPod can go to iOS 2.2 via iTunes and iOS 3.1.3 via

Purchasing iOS 3.1 Software Update for iPod touch (1st generation)       

https://buy.itunes.apple.com/WebObjects/MZFinance.woa/wa/touchLegacyLandingPage

Then:

iOSSearch - search the iTunes store for compatible apps.

Vintapps 3.1.3 - paid app.

Apple Club - filter apps by iOS version.