Q: How to update my iPod

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.

- A 3G to 5.1.1  Requires iTunes version 10.5 or later

- A 4G to 6.1.6  Requires iTunes version 10.7 or later. For a Mac, that requires a Mac with OSX 10.6.8 or later

- A 5G to iOS 7.1.1 Requires iTunes 11.1 or later if you update via iTunes

Identifying iPod models