Aside from extending the life of and preventing damage to the mouse, properly cleaning a mouse will make it easier to use and prevent the cursor from "jumping around" on the screen due to dirty rollers.
Before cleaning, shut down your PC and remove the mouse from the computer. If you're using a wireless mouse, simply powering off the PC will be sufficient.
Note: An optical mouse, which uses a small laser to track movement, does not have a mouse ball or rollers and does not need the kind of cleaning that a "classic" mouse does. With an optical mouse, simply wiping clean the glass on the bottom of the mouse that houses the laser is usually enough of a cleaning process.