One of the first things you need to do when you get a kitten is to litter train him. Litter training a kitten is a whole lot easier than litter training a cat as it hasn't had the chance to get into bad habits.
When a kitten is tiny, it's handy to have a crate or cage where you can shut him up safely at night and when you're out of the house. Make sure that he has something soft to sleep on like an old towel or blanket as well as food, water and the all important litter tray. The cage is now his own little territory where he will feel safe and secure.
When I've raised tiny kittens, I've found that a seed tray is big enough initially to use as a litter tray and a seed tray doesn't take up too much space in the cage. You'll easily be able to tell when the kitten is growing out of it and needs a full sized litter tray.
Litter training a kitten is usually quite easy as cats are very clean creatures. When your kitten comes to stay, gently put him in the litter box straight away. He may not need to use it but it's amazing how he will immediately seem to know what it's for.
Continue to pop the kitten into the litter box at intervals throughout the day if he doesn't go to it of his own accord. If he does have a little accident in the wrong place, just pick him up and put him in the litter tray anyway, even if it's too late.
Feed your kitten regularly and after meals take him to the litter tray; he'll soon learn to do his business there.
In the last couple of years I've raised two kittens. The first one was only three weeks old and in her first few days with us, she did have a little wee in the wrong place a couple of times but the second one, who was five weeks old when we got him never had an accident at all and immediately took to his litter tray.
If you're raising a very tiny kitten which is still being bottle fed, you may need to encourage his first toilet. Take a piece of damp cloth or kitchen paper and gently massage his little bottom. He may just wee a small amount at first and his excrement will be a bit like the consistency of toothpaste. After the first occasion, he won't need any further encouragement.
Do make sure that the litter box is cleaned at least daily as a fastidious kitten won't use a dirty tray and will do his toilet elsewhere.
Litter training a kitten isn't hard but you need to be vigilant while he's tiny and confine him to a small space when you're out or at night so that he isn't tempted to ignore the litter tray.