In perfect case a kitten stays with its mother and other kittens from the same brood for 3-4 months. People, looking after it, treat the kitten kindly and after some time it has got used to your household, that is a monster in the closet (a vacuum-cleaner); the storm in the box (a dish-washing machine); a very active creature without hair constantly dropping food (your baby).
When you come to choose a kitten, look around. The house or the apartment should be clean and tidy. The same with the shelter if you are going here.
If possible examine the mother-cat because its genetic peculiarities and the features of character will influence your new friend.
And now the most interesting step - the meeting with the kittens.
First calmly keep your eye on them and notice that kitten which has come to you to examine and to greet. The kittens which have natural inclination for people, will become the best domestic animals. Small kittens are not sure to feel such interest than the older ones. Bring a toy with you and it will give you a chance to choose the most active kitten. If they are trained to be with people, they will be happy on your knees and feel comfortable into your arms. But if they are frightened and turn to stone with fear when you are taking them, you'd better not to choose anybody. There are many other kittens in the world.
Even if a shy kitten, hiding in a corner, touched you deeply, let it stay in the corner. A shy kitten usually turns into a shy cat. I doubt whether it will be pleasant to feed your pet or to clean its toilet if you see it seldom. That's why such kitten is not worth taking. If all the kitten from the same brood look watchful, take no one.
Every single minute remember that you are binding yourself to take care of your pet for almost 20 years. That's why there is no need to choose the first kitten, you'd better take the kitten you've been dreaming for. Every year millions of kittens look for their owners. An ideal friend is waiting for you somewhere, be patient!
Don't take a kitten which runs away, spits or shrinks in a corner, or scratches and bites when you are taking it in your arms. Choose a real friend instead, which enjoys your company and likes to seat on your knees. If a kitten purrs when you are taking it, it is very good.
Choose healthy kitten. You can easily distinguish such kittens. They are active, with shining hair, sparking eyes and do not have any secretions from their nose. They are thin, but not skinny or big-bellied. It's very important to choose a moment when you're going to look at the kitten, because you may take sleepy kitten for inert and dull by mistake. Small kittens play a lot and sleep a lot like many other small creatures.
You have to choose adult cats taking into account the same rules. Before it just sit down and imagine what you want your ideal four-legged friend to be. Should it be active and plays pranks all the time? Or you want it to behave with dignity and to look at you with understanding? Must it love people or be estranged? Try to have an idea about the qualities of the pet you want to have and then it will be easier to choose a cat suitable. If you find it difficult, try to recall all the cats which have been making you glad during your life. Which qualities did they possess?
After this you are ready. It is easier to deal with adult cats 'cos to some extent you'll get what you see except she-cats in condition of hunting. Such cats and pregnant cats are very friendly and full of love. But it doesn't mean it will be the same after sterilization. You are going to have it sterilized, aren't you? (See: Neuter and Spay). Though, that doesn't mean it is sure to change either.
Choose that very cat which behaves the way you'd like it to. It's not an easy thing to find such animal, especially in shelter for cats, 'cos there a cat may be scared or confused. All in all this is a very good rule. If you are lucky to find a cat which is friendly, calm and ready to play in such surroundings, you may be sure it is your cat in fact. These qualities may be developed stronger when it finds itself at home.