It is extremely important that you prepare a small separate room with the necessary equipment that your new friend will need. Litter box, toys, bowls for food and water, and a comfy bed. Make sure there is nothing that can hurt him/her or anything that can be swallowed. Let your new companion adjust to this room and you need to go in many times during the day and evening in order to bond with him/her. Teach your children to be quiet and gentle during this time. DO NOT give your cat/kitten more freedom to explore or else it will only interfere with their integration into your household, no matter what you might otherwise want to do. Be patient and approximately 5-7 days when you find your cat feeling pretty content with you and happy to see you when you enter the room, you can carry your new friend around your home while she begins to get accustomed to her new surroundings. Try to get her comfortable on your lap while you watch TV or read a book. We all love lap cats! In a few days you can leave the door open to her room and watch her progress as she explores on her own. By the way- keep toilet seats down to prevent accidental drowning- especially important with a kitten.
When getting a new kitten or a cat that was not lucky enough to be properly socialized in their new indoor home- a scratching post is a must. Show him/her how to do it by rubbing its paws on the post(simulate scratching) and he should quickly get the hang of it. Multiple scratching items are well worth the expense to keep your furniture from damage. If they try scratching in an inappropriate place, quickly say no and bring them to their scratching post. Like children they need to learn, and remarkably they learn quickly! Also, get them used to having those nails clipped-the earlier you do it-the more they will get used to it.
When introducing your new companion to other pets you may have, during the adjustment time in the small room, place a towel with the scent of your other cats and dogs so he/she can be familiar with their scent. Do this for your other pets as well with the smell of your new addition. They will appreciate being keyed in to these new scents before they finally meet. Remember when introductions are finally made to never force them together or leave them alone together. Always supervise and you will see when they adjust to each other in time.