When you bring home your new kitten you want to integrate your new kitty into your life as easily as possible. If you live alone it will be easier to incorporate your new kitten into your home life. If you have pets already and other family members such as particularly small children then it makes it a little more challenging.
There is a little trick you can do before bringing kitten home if you do have a pet already to make the homecoming less stressful for both animals. What you do first is take a small hand towel and rub your current pet down with it. The scent of your pet will be imparted on the towel. When you go to take your new kitten home you put that same towel in the carrier with the new kitten so kitten can smell the pet you have at home.
When you arrive at home with the new kitten you then take a towel and rub the kitten with it and give it to the current “Master of the Home” pet. This way your current pet will smell the new kitten too. You do not let the new kitten loose when you get home. You find a confined safe space to introduce the two pets to each other. Before you show the current pet the new kitten you give them the towel with the kittens scent again so they won't react as aggressively as they would without recognizing the new baby's scent.
Make the two pet’s first introduction short for the first few times. Basically show your older pet your new kitten and soon after remove your kitten.
It takes about two weeks for two animals to adjust to each other. Gradually increase the time between the two but keep it supervised. Bringing home a new kitten can be very stressful for an older established pet. Do not fuss over the kitten when the old pet is present and lavish as much attention on the old pet so he or she does not feel displaced.
The same way you introduce your new kitten to your older pet is the same way you introduce it to the rest of your family. Gradually at first. If you have small children you need to sit them down and lay ground rules of what is acceptable and not acceptable behavior with the new kitten. They need to understand that the new kitten is not a toy. It is a living creature and needs to be handled with care.
Make it clear that they are not to tease, chase or hurt the kitten in any way. This means when the kitten eats, sleeps and uses the litter box they should not bother the kitten either. Make sure they understand not to pull the kitten’s tail, ears or use any kind of hurtful behavior towards the kitten. Show them how to correctly hold the kitten. Time they spend with kitten should be supervised especially when their friends come to play.
Once your kitten gets used to the environment, your family and your other pet/pets accepts kitten it should be smooth sailing. Don't forget to spend a lot of time with your new kitten so you can bond with him or her as well. The quicker you two bond the better it is for you to train kitten and the more affectionate kitten will become to you and your family.