Cats, more than most other domesticated animals, are attached to their environment as well as to their people.
Being a small animal which is vulnerable to many dangers (dogs, coyotes, cars, dangerous people), cats learn how to keep themselves safe in their home environment—so when the cat's home changes, it can be tough for her to adjust. However, when you adopt a new cat, there are several things you can do to help her adjust and feel safe in her new home.
Provide a Safe Place
Before you bring your new cat home, set up a safe place for her that will be just for her. Make sure the resident cat, dog, ferret, or whatever cannot intrude. A second bathroom or laundry room will work. When I brought home my two new cats, brothers rescued from a feral cat colony, I set them up in my guest bedroom. With places to hide (a cat crate, a cardboard box on its side, and several cat beds) and no other pets in that room, they could get used to the sounds and smells of the household without feeling threatened.
Make Sure the Spot is Ready
Have that safe place already set up before the cat comes home. If you're moving around too much, moving this, rearranging that, pouring out litter, and doing all the other things while the new cat is in the room, she may panic. Instead, with everything set up and ready for her, you can just sit quietly in the room with her for a little while. She can watch you while you're sitting quietly watching her.
The First 24 Hours
When you bring your cat home, take her directly to her safe room. Don't show her off the neighbors or allow everyone in the family to hold her. This can be too frightening and could cause her to distrust everyone. She may also panic—clawing, biting, and even trying to escape. Instead, take her to her room, close the door, and open her carrier door. Then sit quietly with her. Let her come out when she's ready. If she comes to you, great, just touch her carefully and gently. However, she may want to explore her room or more commonly and look for a hiding spot. Let her hide; it's okay. Just come in and sit with her several times during the first day. Talk to her, read a book, or just relax.
Be Patient when Petting
Cats rarely want to be handled (and especially, hugged) by strangers. Give your new cat time to get to know you. I let Spock and Scottie, my new cats, watch me for several days before I tried to touch them. Then I just touched one finger to a cheek and rubbed briefly before stepping back and giving them space again. It was a week before I ran my hand down each cat's back once each. By giving them space and being patient, though, I built up trust. The cats learned to trust me and now, two months into our relationship, I can touch them without any reservations.
A Screen Door is Great
After two weeks, when my new cats were comfortable in their safe room, I bought an inexpensive screen door and mounted it on the door to the cats' room. This way my dogs could look in and watch the cats and the cats could be safe in their room and watch the dogs. I kept the screen door closed for a couple more weeks until everyone was used to each other. Then even when the cats were allowed free run of the house, I would put the cats in their room at night, or when guests came over, or when I vacuumed the house; any stressful situation where they might panic. Since I feed the cats in this room, they don't need convincing to go back there.
A Baby Gate Maintains Safety
When your cat is comfortable enough that you'd like to let her explore the house, prop the screen door open and put a baby gate across the doorway positioned about eight inches from the floor. This way, once the cat is exploring the house, should she be frightened, she can dash under the baby gate to the safety of her room. This works well if the family dog or the kids in the family get too rowdy. In addition, the baby gate can help keep the family dog out of the cat's food and litter box. She can also come and go under the baby gate to eat, drink, and use the litter box.
Introducing Your New Cat to the Family Dog
Even though cats and dogs can become good friends, don't expect this to happen right away. Instead, teach your dog to leave the cat alone. He is not allowed to chase the cat, play rough with her, pin her down, or do anything else that could scare her or potentially injure her. Use your dog's obedience training, put him on a leash, and while he does a sit or down stay while you hold his leash, let the cat out of her room. Should he get over excited, take him away from her. If he controls himself, let him watch her. Repeat this as often as needed until your dog understands the rules. Keep in mind that dogs with a strong prey drive (those who like to chase and catch small animals) can be a danger to cats.
The Power of Toys
Many cat rescue organizations send toys home with a newly adopted cat because they know that play will help a cat relax, bond with the new owner, and will let the cat relieve any stress she's feeling. Flirt poles (miniature fishing pole type toys with a cat toy that can be dangled or flipped in front of the cat) are especially fun and can encourage even the shyest cat to play. Cardboard boxes, paper bags, balls with bells, and feathers are all good toys. Some cats are attracted to catnip (not all cats are) and for these cats, a little catnip on a scratching post or cat tree will provide your cat (and you!) with some great fun.
The key to helping your cat adjust to her new home and family is safety; she needs to feel safe. If she feels threatened, if the dog chases her, if the children pick her up at every opportunity, or if something else makes her feel unsafe, adjustment will be slow. So concentrate on letting her progress when she's comfortable, coming out of her room when she's ready, and interacting with people when she begins trusting them. You'll find that she'll adjust more quickly when allowed to do so at her own speed.