Its Easy. Just connect your device to wifi if you want to save data transfer cost and Go to Settings > General > Software Update If the update is available select download. Once its downloaded you can install it.
You can also leave download in the background and you will get notification once it is complete.
Keep your device switched to power source to ensure the download and installation is sucessful
If for some reason an OTA update isn't viable for you, you can only update with the same computer your iPod to. Any other computer you connect your iPod to will not do it unless you erase the iPod and register it with that computer.