Kittens should stay with their mother until six or eight weeks of age. They need their mothers milk to survive, and learn a lot from their mom before going off on their own. You can then take that 6 week old kitten home and provide it a safe, warm, comfortable place to live with plenty of food and water and a clean cat box. Cats are pretty solitary animals and actually like to be left alone. Make sure to visit the vet with your kitten for all the shots it will require to remain disease free.