how to update ios through itunes for an older ipod touch?

Update it as described in this article, or this one if it's a first generation iPod touch.

The maximum iOS version for the first generation iPod touch and original iPhone is 3.1.3.

The maximum iOS version for the second generation iPod touch and the iPhone 3G is 4.2.1.

If you don't know what device you have, append the last three characters of its serial number to http://www.everymac.com/ultimate-mac-lookup/?search_keywords= and load the page.

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 you have the original (1G) iPod. That model does not have volume buttons on upper left edge and does not have a built-in speaker