One other note - an iPod cannot contain music from two computers. If you switch computers, the old music on the iPod is replaced. However, up to five computers can be authorized to share music purchased from ITMS, so that can provide some flexibility.
Wrong, your iPod can contain music from as many computers as you want. However, you cannot have it automatically sync to more than one. If you are willing to manage it manually (i.e., drag songs from the Library list to the iPod icon in iTunes), then you can connect it to as many computers as you wish.
It's in the preferences. Connect your iPod to the new computer. iTunes will pop up a dialog box that says (in effect) that this iPod contains the music library from another computer and would you like to sync it with this one? Click NO, and then go into Preferences (under the Edit menu on Windows, under the iTunes menu on Mac). Click the iPod tab (Windows) or icon (Mac) in the Preferences window that appears. Click the button to "Manage music manually" (or similar - I forget the exact wording, but it will be the bottom radio button in the window. Click OK and close the window. You can now use your iPod with as many computers as you so desire.
It takes more time to describe it than it takes to do it.