Connect the iPod to your computer and update via iTunes
A 1G iPod can go to iOS 3.1.3
A 2G to 4.2.1. Requires iTunes version 10.X. That requires a Mac with OSX 10.5.8 or later. With 1OSX 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. That requires a Mac with OSX 10.6.8 or later
Are you sure you really do not have a 2G iPod? Those can only go to 4.2.1
iPod touch (3rd generation)
iPod touch (3rd generation) features a 3.5-inch (diagonal) widescreen multi-touch display and 32 GB or 64 GB flash drive. You can browse the web with Safari and watch YouTube videos with Wi-Fi. You can also search, preview, and buy songs from the iTunes Wi-Fi Music Store on iPod touch.
The iPod touch (3rd generation) can be distinguished from iPod touch (2nd generation) by looking at the back of the device. In the text below the engraving, look for the model number. iPod touch (2nd generation) is model A1288, and iPod touch (3rd generation) is model A1318.