To backup see:
When you restore the iPod it will also be uopdated.
Connect the iPod to your computer and update via iTunes
A 1G iPod can go to iOS 2.2 via iTunes and iOS 3.1.3 via
A 2G to 4.2.1. Requires iTunes version 10.X. If a Mac it requires 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. For a Mac, that requires a Mac with OSX 10.6.8 or later