How do I find out what generation my iPod touch is?

Append the last three characters of its serial number to http://www.everymac.com/ultimate-mac-lookup/?search_keywords= and load the page.

(85582)

I am a real fan of Everymac.com, but they don't always use the same names that Apple does. For instance, if you enter MC086LL/A into their search, you will get an unofficial name for that iPod which has caused a lot of confusion.

Here's Apple's identification guide:Identifying iPod models