When you get to the shelter, take a quick walk through the cat room before stopping to visit with any one cat. See how each cat reacts to you walking by, and pay attention to those who seem to be interested in meeting you. Watch to see which ones come up to the door and try to smell you or rub their faces or bodies on the door. Once you have found a cat that you wish to meet, ask the shelter staff if you could spend a few minutes in a quiet place with that specific cat. Pay attention to the cat's personality: Does he like to be petted, or picked up? Is he interested in you? Don't be afraid to ask the staff a few questions about the cat you are about to choose: Ask about his history, does he get along with the other cats and dogs, and ask their opinion about him. Don't forget to ask about any medical history as well.
When you bring him home your new companion, designate a small space for him to be for a few days, like a laundry room, or a bathroom. Cats are territorial and your new cat will be uneasy and afraid in a new place at first. In his own room, include food, water, a bed, some toys, and a clean litter box. It wouldn't hurt to put one of your old t-shirts on his bed so he can become accustomed to your scent. When initially spending time with your new cat, be patient. He might not come up to you for a little while, but give him his space and he will get acquainted on his own time.
If you have other pets in the home, don't attempt introductions for at least 4-5 days. Let your pets smell underneath the door and acquaint themselves by smell at first. The first time the two pets meet face-to-face should be short and calm, introduce the pets by opening the door just wide enough so they can see and smell each other. Be certain that you stand close by to supervise. This should be done for a few days.
If you have children in the home, the American Humane Society recommends adopting a cat over 2 or 3 years old. Young children tend to be very active and may be too rough with fragile kittens, which can result in injuries to the kitty and/or a fearful, skittish adult cat. To formally introduce both cat and child, ask your child to hold out one finger and allow the cat to sniff it. If he tries to rub your child's finger, that is a great sign! If he backs away or hisses, he is not comfortable, and try again another time. If the finger test went well, your child can gently start scratching his head, neck, chin, and pet him on his back. Make sure to establish ground rules with your children, like do not squeeze him, or pull his tail, explain that cats generally don't like their bellies rubbed or to be held very long.
Your cat should have his first wellness visit at a vet within a week of his adoption. Be sure to bring any medical documents including spay/neuter, and immunizations. Be sure to keep him on the same food the shelter was giving him, and if you plan on changing the food in your cat's diet, do it gradually.