How do you teach a kitten to use the litterbox?

We have 8 cats.
When you get your kitty in, the first thing to do is find a room where you can keep her a few days, so that she will become oriented to a small space in the house before being introduced for a big confusing space. Put the food and water on one side of the room, the litterbox on the other side of the room, and the bed somewhere in between. Make sure and come in often for play, petting, general love and reassurance.
The first rule of kitty elimination is that cats hate to eat where they "go" and they hate to "go" where they eat. If you put the food and water next to the litter box, you will have committed the most common mistake that cat owners commit, which is the single biggest cause of kittys going elsewhere. A kitty would rather risk going somewhere else than risk contaminating their food, so your best bet is to keep the food and water either to the opposite side of the room from the litter box, or, even better, (once you have let her out of the room) to a different room altogether from the litter box. Then make sure you have at least 2 – 3 inches of litter in that litter box and that you keep it scooped and clean. Kittys also hate not enough litter, and they hate dirty toilets. You wouldn't like going in a dirty, smelly toilet. Neither do they.
We have 8 cats, have had up to 11 – at ages all the way up to 19 years old, all are indoor kittys, and this method has worked like a charm. Six of these kittys were trapped wild and tamed, and oriented to the litter box this way. All respect litter box rules.
One last note: Kittys seldom respond to punishment. They are unable to associate punishment with behavior – especially if it is after the fact. They do, however, respond to positive reinforcement.