Iffen ya really don't wanna take Spaw's good advice (and it is!), underneath yer mouse is the ball. The ball is held in place by a ring with a hole in it. Open up a paperclip and put the long end in the hole, then rotate one way or the other and the ring will fall off. The ball will fall out.

Spray the inside with some canned air (don't use a compressor!), or blow the dust out with a straw. You can gently wipe the inside with a tissue, too.

Clean the ball by gently rubbing it with a tissue (it's hard rubber, most likely).

Now put everything back the way you found it.

Bobert, even you kin figger out how to do that.

Then consider how danged BIG the mouse was who originally owned that ball.