Take your kitten to its kitty litter box right you take it home. Sometimes that first visit is all is needed. But until you're sure that the kitten understands, take it there after each feeding. Sometimes felines will not use a kitty litter box if something about this make of litter is never to their liking. Once in a while they will prevent the package if its location is not private enough. Make an effort to solve these problems if the kitten does not use the kitty litter box from the start.
The veterinarian will also take a look at the kitten for indicators of disease. Bring along test of the kitten's shedding so that the doctor can look for worms.