Introducing your kitten
Moving to a new environment with a new family is going to be stressful, it's best to minimize the stress where possible and be patient. A swift change in food can upset an already stressed kitty leading to diarrhea and vomiting. If the food selected in the new home is different than the old one it should be changed slowly and progressively, not abruptly. Unless the change is to or from raw because raw can not be mixed with dry kibble.
Changing litter can be followed much like the food. Kitty
may not want to use a completely different litter, mix old
and new to entice kitty or use the cat attract litter for the
first couple of weeks in the new home.
Set up your bedroom for the new kitty room, base camp.
Provide a warming pad or heated pet bed in the room and
anything the kitty may need: litter box, water, scratching
post, blankets, toys... A small space helps them feel more
Keep the kitten shut in this new sanctuary away from any other pets for a period of one week. Animals can sniff under the door, but no meeting yet. After a week begin to bring blankets or toys with scents from other animals and let the new kitty sniff them out, Do the same for the other animals. Place the new kitty in a kennel and bring it to the center of a room with the other animals, let them sniff out the kennel and watch the reactions. Washing all the pets in the home with the same scent can help, they tend to like similar smells.
If the home has 2 cats then there should be 3 litter boxes and an extra litter box for each additional cat. Make sure they are easily accessible, not off in a corner and not in a cold place.
Best bet is always: get a pair together.
Signs of stress and what to try:
lack of appetite: have a high-calorie nutrient gel tube on hand before kitty arrives, this works wonderfully on enticing kitty to eat or at least lick up some calories, cats just can't say no to this yummy treat. Then try some all meat baby food jars with a little dab of gel on top.
getting a cold: the kitty should come with a health guarantee and it is important to see a vet within the first 48 hours to verify health; however, with the stress of moving and traveling like us kitty can get a little under the weather especially if flying alone. Make sure kitty is eating, drinking water, stools are formed, eyes are clear. Keep them warm. Use some baby nasal saline spray if need be to rinse out the little noses.
hiding: this is a fear response. Keep kitty in a small area, confined to feel secure in the kitty oasis/base camp.
aggression: specifically hissing, mostly directed towards animals. This is normal in the beginning and should lessen over time. Monitor and limit interactions with animals in the beginning.
not using the litter box: could also be fear or just preference. Some cats won't use a covered litter box, some will. Use the same litter the kitten was already accustomed to and slowly transitions as discussed above, also the cat attract litter can help. If kitty just won't use the box then kitty will need to be confined to a very small area for 14 days with a litter box for retraining.
Article by Animal Planet about
introducing a new cat to an old cat
Jackson Galaxy has some good tips
and tricks also found on youtube