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If it's really thin, and it has volume controls on the side, it's a 2nd gen. If it's thicker, and the bezel ring surrounding the edges on the front is matte rather than really shiny chrome, it's a first generation.
 
If it's really thin, and it has volume controls on the side, it's a 2nd gen. If it's thicker, and the bezel ring surrounding the edges on the front is matte rather than really shiny chrome, it's a first generation.

Actually the 2nd gen is 0.5mm thicker than the 1st. It just seems thinner because of the tapered edges.
 
And the wifi (the black plastic piece on the back) is oval shaped on the second gen, and is more square and takes up the side as well on the 1st gen
 
Aside from the volume buttons on the side, I'd say if you press Play in the Music app and you can hear it without any headphones plugged in, well... ;)
 
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