Q: how do i update my ipod touch version 2.2.1 to the updated ios system so i can download games and apps

To update

The Settings>General>Software Update comes with iOS 5 and later.

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

- A 2G to 4.2.1. Requires iTunes version 10 or higher. If a Mac it requires OSX 10.5.8 or later.

Identifying iPod models

I suspect y have the 1G

To more easily find compatible apps:

iOSSearch - search the iTunes store for compatible apps.

Apple Club - filter apps by iOS version.