I have never tried this so I don't know if it works, but I have heard....

Put your cat and his/her litter box in a small room together for a few days. Cats do not like to soil their environment and if they are confined to a small area will use the litter box to keep the rest of their territory clean.

The big issue here though is keeping the box clean. Cats are clean freaks. They include their toilet in their neatness.

A funny note on how clean they are:
I wear a rubber mouth guard when I sleep because I grind my teeth. I take it out in the morning and brush it because it has "morning mouth." One day I took it out and set it on the sink. I was going to brush my teeth and my mouth guard when I got done in the shower. I pulled my towel off the sink when I was done showering and pulled the mouth guard off onto the floor. My cat came over, smelled it and promptly clawed at the bathroom throw rug and covered it up. I guess she told me.