The First Few Days and Nights
Have a room set up just for your new kitten if possible. Provide them with a cozy carrier as a den and soft fleecy blanket inside (preferably with his/her siblings scents on it. You can ask your foster to do this for you at the adoption). A snuggle toy is also comforting to kittens. There are some available at the pet store or on Amazon that purr which comforts and relaxes your new kitten.
Also provide a litter box with non clumping unscented litter in a box that is not too high on the sides so they can easily get in and out. The box should also be wide enough that the kitten does not step in their own feces and has a clean area to go. The litter box should be cleaned at least once a day and completely discarded and changed at least once a week. Guidelines for litter include using non clumping for the first 6 months due to the fact that kittens may eat it or lick it off their paws. Clumping litter sticks together and can cause a choking hazard for little ones.
Set-up a bowl of clean water and dry kitten food in the room to have available at all times. Keeping the water fresh entices the little ones to drink more water which is often a problem for kitten and cats.
Your kitten may meow quite a bit the first few nights as they are missing their siblings and fosters. Others may hide and only come out to feed and use the litter. Try to keep in simple and let the kitten come to you when she is ready.