Your mouse should have screws on the bottom. If you can't find any, remove the pads on the bottom (the pads to make the mouse slide) and open the mouse up. The PCB inside should pop right out then you can wash the plastic, let it dry and put it back together nice and clean.
If you can possibly get to it qith a Qtip, you can put some Isopropyl Alcohol on the Qtip and use that to clean it. It's best to use the 90-ish% stuff, not the 70%. As close to pure alcohol as you can get is best, that way it evaporates away and doesn't leave a bunch of byproducts.
If that isn't an option, i think you will have to go with ben333's advice and take it all the way apart and clean it. If you aren't real physically technical, you might consider taking a few pictures with a digicam as you dismantle so you know how to put it back together. But it should be fairly simple in there unless it's a fancy wireless mouse or something with 20 buttons.