Well that depends on how thorough you want to be. You can do a superficial cleaning that will require only a toothpick or a key, or a thorough cleaning that will also require a q-tip and some rubbing alcohol and some scrubbing on your part.
First you need to turn off the computer and unhook the mouse. Now you need to remove the ball from the mouse. Turn the mouse upside down and you will see a lock ring holding the mouse ball inside the mouse like in figure 1. Most will turn to unlock but others will need you to apply pressure and pull them off. Either way, unlock the ring and turn the mouse over into your hand letting the ball and ring fall into your hand like in figure 2.
Figure 1

Figure 2

Take a look inside your mouse, at the mouse ball, and at your mouse pad. You will notice that some debris has built up in one or more places; this is what is causing your mouse to act erratically. For a simple cleaning you would shake the debris off the pad and the ball, and use the toothpick or other cleaning device to scrap the dirt off of the rollers inside the mouse like in figures 3 and 4. For a thorough cleaning, after you get the debris off you will want to swab the rollers and ball with a q-tip slightly dampened with the rubbing alcohol. Also, most mouse pads can be washed with lukewarm water and dishwashing soap. Be sure to rinse all the soap off, however. Now set all the parts out to dry for a few minutes then move on to step 3.
Figure 3

Figure 4

Step 3:
Time to put the mouse back together. Place the ball back into the mouse and slide/turn the ring back into place making sure to relock it. Now you can hook the mouse back up to the computer and work with it again hassle free. Congratulations! You should now have a clean mouse.
As always, if you have any questions or need assistance with any problems, please contact the Helpdesk at x5470, menu option #2, or through email at SHV PC HELPDESK.