Apple's range of iPod devices rely heavily upon a partnership with the iTunes multimedia management software when synchronising and backing up content to a computer. The device and the computer must both be logged into the same iTunes account to sync content such as music libraries, videos, applications and playlists. By authorising another computer to use the same iTunes account, the iPod can be synced with multiple computers at the same time.
Download and install the latest version of Apple's iTunes software on your new computer.
Launch iTunes and click the "Store" menu, and select "Sign In." Enter the same iTunes account details as used on the iPod, and click the "Sign In" button.
Click the "Store" menu again and select "Authorize This Computer." Enter the iTunes account details again when prompted, then click the "Authorize" button.
Connect the iPod to the computer using a USB cable. It will be automatically detected by iTunes.
Click the entry for the iPod in the "Devices" menu in the left-hand column, followed by the "Summary" tab.
Click "Sync" in the lower-left corner. All the iPod's content, including its music library, will be synchronised and backed-up onto your new computer, where it will be accessible through iTunes.
Multiple iPods or iPhones can be signed into the same iTunes account as the new computer to share content between them.
If you sign into a different iTunes account on your new computer, it will no longer be able to use the music library backed up from the iPod. Only five computers can be authorised on an iTunes account at any one time. Remember to de-authorise old computers from iTunes before disposing of them.