Kittens learn the appropriate place for urination and defecation by observing and imitating their mothers. True copycats, they will follow their mothers to the litterbox and play and explore in it. Partially by instinct and partially by trial and error, they will start eliminating in the litter box.
Orphaned kittens, therefore, are at a disadvantage. Depending upon their age, you may need to take over elimination-stimulating duties that the queen would have performed. The average kitten begins litter box training between 4 and 6 weeks of age. Litter training may proceed smoothly if there is another cat in the household that has accepted the kitten. The older cat may serve the role of instructor by allowing the kitten to follow it to the litterbox, much like the mother cat would have done.
But if your new kitten has no other feline companions, you will have to show the kitten the location of the litterbox and help it understand what it is there for. It is easier than it sounds. When the kitten starts to explore its environment on its own, you can take it to the litterbox several times a day. Twenty to 30 minutes after a meal is a good time because that's when most animals experience a gastrocolic reflex--increased activity of the intestinal tract that leads to evacuation.
When the kitten is inside the box, stimulate its interest in the litter by stirring it gently with your finger. Let the kitten jump in and out of the litterbox at will rather than trying to restrain the kitten inside. You can also place some stool in the litterbox, which will make it easier for your kitten to associate the litterbox with elimination.