If your computer is off, just plug the mouse in and turn the pc on; the mouse should be recognized during boot - if kudzu (the hardware configuration demon) ask you to configure a new device, answer yes and follow the steps.
If your computer is already on, log out and then switch to a virtual console (ctrl+alt+F1), login as root and type
plug the new mouse in; type
select from the list the option most suited to your model and confirm; type
You'll return to the graphical login with the new mouse working.
Return to the virtual console and logout; hit ctrl+alt+F7 for the graphical login.