Q: 2nd generation upgrade

Update it from iTunes on a computer as described at the bottom of this article; devices running an iOS version prior to 5.0 can't be updated straight from the device. It will be updated to the newest iOS release supported by the device’s hardware.

The iPhone 3G and second generation iPod touch can’t be updated past 4.2.1.

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Are you sure you have a 2G iPod? A 1G (original ) iPod touch can only go to ios 2.2 via iTunes. It can be updated to as high as 3.1.3 by:

Purchasing iOS 3.1 Software Update for iPod touch (1st generation)       

https://buy.itunes.apple.com/WebObjects/MZFinance.woa/wa/touchLegacyLandingPage

Identifying iPod models

The 1G does NOT have volume buttons on the upper left edge.