Your iPod charges while plugged in to your computer. However, if it doesn't show up in iTunes it won't sync and you can't manage your content. This is usually a simple problem that can be fixed by checking all hardware connections and restarting where necessary.
Unplug your charger cable and plug it back in again. Make sure it's plugged into a USB 2.0 (high powered) port, rather than on a secondary device such as a keyboard. The high-powered port is required to correctly interface your iPod and computer.
Install the most recent edition of iTunes and restart iTunes. Sometimes opening iTunes while your iPod is already plugged in will force iTunes to recognise it. Otherwise, open iTunes after installing any updates and then plug in the iPod again.
Restart Your Computer
Restart your computer to rule out any latent glitches. This often resets the "order" in which your computer recognises things so that your iPod will be correctly recognised. Make sure you unplug your iPod before you restart.
Let iPod Charge
An iPod that is almost completely or completely drained of battery may not be recognised by your computer. Check the screen for a "very low battery" warning when you plug it in, and let it charge for half an hour before trying to get iTunes to recognise it.