Q: How do you do the update with a iPod touch 1

If you have the 1G 9Original iPod touch) those can only go to 3.1.3

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.X. If a Mac it requires OSX 10.5.8 or later. With OSX 10.4.11 you can only go to iTunes 9.X which gets you as high as iOS 4.1

A 3G to 5.1.1  Requires iTunes version 10.5 or later

A 4G to 6  Requires iTunes version 10.7 or later. For a Mac, that requires a Mac with OSX 10.6.8 or later

Identifying iPod models

If you already have iOS 3.1.3, and that is as far as you can go, you won't be able to download an app that requires a newer version of iOS.

Try to find an alternative:

Finding iOS Apps Compatible with Older Devices