how do I update iOS to 3.1 on ipod touch 1st generation?

Hi

I want to be able to put games on my ipod 1st generation touch so my 5yr old keeps his sticky mitts off my iphone! Ive read the software needs to be updated to iOS 3.1 so that the App Store appears on the touch (at present the version is 1.1.5) Ive also read that you go into itunes store and purchase this update for a few dollars. Probably me being stupid but I searched on itunes store and cant find it.

Please can anyone tell me if Im following the correct and easiest way of being able to put some free games on the ipod touch and if I am, where/how do i update the touch so the App Store appears

Many thanks in advance

Best wishes

Simon