This article explains how to turn off an iPod nano. Instructions apply to the 7th generation iPod nano and earlier models.
How to Turn Off an iPod Nano and Save Battery Life
To turn off the 7th generation iPod nano or 6th generation iPod nano, do the following:
Press and hold the Sleep/Wake button (located at the top right of the nano). A progress wheel will appear on the screen.
Press and hold the Sleep/Wake button until the screen goes dark. The nano is now off.