Take your kitten to its kitty litter box as soon you bring 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 pet cats will not use a litter box if something about the particular brand of litter is never to their liking. Sometimes they will all the container if its location is not private enough. Make an effort to solve these problems if the kitten will not use the kitty litter box right away.
The veterinarian will also examine the kitten for indications of disease. Bring along sample of the kitten's dropping so that the doctor can look for worms.