The iPod line of digital music players became famous for its ease of use, but that doesn't mean it's without its quirks. A variety of deals and concessions with the recording industry means the iPod can only receive files from a single computer---the one it's registered with. So whether you've purchased a used iPod still registered to another computer, or bought a new iPod and want to transfer its registration, your only option is to reset the iPod to factory settings and then re-register it.
One Computer Per iPod
In order to attract record labels to its platform, Apple needed to prevent the iPod from becoming an extremely portable file sharing device, Apple imposed certain restrictions, such as you need to register your iPod with one computer in order to use it.
If you plug your iPod into a computer other than the computer it's registered with, you'll be limited in what you can do. That computer will be able to play music from your iPod but will not be able to transfer music to the computer. That computer will also not be able to copy music from the iPod.
Restore to Factory Settings
In order to use your iPod with a computer other than the one it's currently registered with, you need to re-register the computer. Unfortunately the only way to do this is to restore the iPod to factory settings---completely deleting all music and settings on the iPod. If you're transfering your registration from one computer you own to another, make sure all your music and data is on that computer before proceeding---you can transfer the data directly from computer to computer later. If you recieved the iPod from a friend or purchased it used, there is no legal way to transfer the music from the iPod to your computer.
Open iTunes and plug in your iPod. Click your iPod to check out its music and settings, then click the "Summary" tab. Click the Restore button, and select your prefered method of restoration---"Restore and Update" is recommended if you're not sure.
Connect to New Computer
After following these steps, connecting your iPod is easy---just plug it into the computer you want to use it with and, assuming iTunes is installed, you'll be prompted to register the iPod as though it's brand new. Follow the on-screen prompts to set up your iPod with its new computer.