Kitten training is very simple when it comes to the use of the litter box. Even newborn kittens are inherently driven to bury their feces, so very little effort will be necessary on your part. If the mother cat is available, you will need to do even less, because she will show them where the litter box is and what to do there. If they need a little encouragement or there is no mother cat, there are some things you can do to help them and get your kitten training off to a good start.
Ensure that the litter box is low enough that the kittens are able to climb into it without a great deal of effort. Most litter boxes for adult cats have outer walls that are too high for a kitten to crawl over, and a kitten who can not get into the litter box on its own is a kitten that will not be using it at all.
Use a plain, simple, non clumping kitty litter. Kittens are sooner to eat a bit of the litter when they are learning, and the clapping varieties are very dangerous if ate. It binds up in their intestines and can cause serious medical problems.
Just like when potty training a child, privacy and safety are important if the kitten is going to be able to "perform" and learn what to do. Place the box in a quiet, out of the way place that is also a good distance from their food and water bowls. Just like you would not want to eat in your bathroom, neither would they.
Place the kitten in the litter box periodically through the day when they would normally need to relate themselves. Mornings, after waking up, and after eating are a few of the most common times, and good times to start. After placing the kitten in the box, gently take their front paws and scratch at the litter. It may take a number of tries before they get the idea, but they will.
If your kitten relieves him or herself outside of the litter box, punishment will most likely be ineffective at best. Kitten training involves a surprising little amount of punishment when compared to other pets, such as dogs. Their minds simply work differently. Just pick them up and put them in the box when you see them starting to go. They will learn before long.