A new kitten will best adapt to a new environment by spending the first few days in a quiet room with a cozy bed, food, water, a litter box and a scratching post. Kitty will also thrive on your gentle attention, so visit her often to play and cuddle.
The room should have plenty of places to hide and explore so that the kitten feels more secure. If not, provide an open cardboard box or two. Electrical cords and window blind cords should be tied up and placed out of reach, as curious, active kittens will likely get into trouble with them. As a general rule, cats don't like to eat next to their litter box, so make sure the food and water bowls are on the other side of the room from the box.
During this transition time, introduce the kitten gradually to other household members. Interactions should be calm and the kitten should be handled gently. Children can be encouraged to pet softly, and to pick up the kitty carefully, with one hand behind the front legs and the other supporting the rear legs. Introductions to other animals should also be closely monitored and taken slowly.
After a few days, the kitten can explore other areas of the house. If she still seems nervous, the kitten can be moved using the carrier and allowed to explore each room one at a time. If she seems ready to explore, allow her full access to the house under close supervision. Watch for items like rubber bands, deflated balloons, small jewelry pieces and Christmas decorations, as they can be very hazardous to kittens. Toilets can also pose a danger, so make sure lids are down in all the bathrooms.
Most importantly, a new kitten requires love and attention. These key elements will allow her to thrive and feel safe in her new environment.