This article is from the Care of Orphaned Kittens FAQ, posted to rec.pets.cats newsgroup. Maintained by Sharon Talbert with numerous contributions by others.
Kittens are like any other toddler; they play too hard and too long and then desperately need to relieve themselves, so be sure a litterpan (or litterpans, in a larger room) is handly at all times. Start with a pan small enough and low enough for a toddler to get into (and out again) with no trouble; a good starter pan is the cut-down box used in pet food stores for display of small tins. Very little training is necessary. Put the kitten into the litterpan 15 minutes or so after a meal, perhaps stimulating it by guiding its paws into a digging motion. If the kitten hops right out, put it right back in again, at least for a time or two. That and the occasional remainder is all you should have to do. If there is an accident, put the feces in the litterpan to help redirect the kitten. Use newspaper rather than plastic on the floor. And do NOT use clumping litter for a young kitten! Kittens are likely to eat litter, and the clumping stuff can block the intestine. I recommend a pellet-style litter until the kitten is at least eight weeks old, and even then watch to be sure the kitten is not eating the stuff. When the kitten is five or six weeks old, it is ready for a full-size litterpan; simply provide a brick as a stepping stone if necessary (I wrap the brick in an old towel).