No Existing Pets
If you have no other household pets, integrating a new kitten into your home is a fairly simple matter. You'll automatically make her one of the family and will no doubt spend a great deal of time with your kitten, bonding and generally "spoiling" her.
However, keep in mind that your home is a strange new place to your kitten, and depending on her background, she will need time to adjust and explore.
She may have come from a foster care situation where care was taken to bond her to humans. On the other hand, many kittens spend their early weeks in a shelter - either in a cage with littermates, or in a "room" setting with a number of other cats, young and adult. In the latter case, your new kitten will require lots of love and patience, plus the chance to be alone when she requires it. Your care in providing these needs will help ease your kitten's fears about her new environment.
An excellent way of starting the bond with your new kitten is to practice the "gentling" technique, detailed in "How to Gentle a Kitten." I can't take credit for this content. It was given to me by another About Guide who got the information from her veterinarian. This technique not only helps the bonding process, but also gets the kitten accustomed to being handled, which will be invaluable later with dental care, brushing, and veterinary examinations.
Set aside a private area, with a bed, food, and a litter box for your kitten. It doesn't have to be a whole room, but can be a corner screened off from the room's normal activity. We call this a "Safe Room."
Give your new kitten space when she needs it, lots of loving attention when she asks for it, and she soon will feel at home with you.
Integrating With Other Pets
It's another matter entirely, however, if you have existing dogs and/or cats in your family. First, it's important to quarantine the little newcomer(s) until they have had their veterinary exam, to prevent spreading diseases or parasites they may carry. Feral kittens often have ear mites, fleas, and other parasites. Sadly, they may to be carriers or be infected with FIV or FeLV. Kittens adopted from shelters quite often have URIs (upper respiratory infections), including Bordetella (kennel cough). Even kittens from breeders occasionally may have the former, as often URIs have an incubation period of up to three or four weeks, thus even a reputable breeder may be unaware of this condition in a newly adopted kitten.
So, put your kitten in a separate Safe Room (see above) for a couple of days. Make sure she has her own bed, food and water dish, and litter box. After she has been cleared by your veterinarian, you can open the door to her "safe room" a crack, to allow the other cats to sniff and peek at her. Rub her with a towel to impart her scent on it, then put the towel in the sleeping area of your existing cats, so they'll become accustomed to her smell. Reverse the tactic by giving her a towel or blanket with the scent of your older cats.
In a couple of days you can put her in a carrier and allow the other cats to come in and sniff her. Expect a bit of growling and hissy-spitty behavior at first; it's instinctive.
For "holdouts," try not to rush things, but provide occasions where the older cats and the new kitten can share pleasurable activities. My cats enjoy playing "chase the ball" with little Billy. The "ball" may only be a crumpled up piece of paper, but it offers interactivity as the cats compete to be the first to bring down the "prey." It's surprising sometimes how often they let Billy "win."
Soon-- within a week or two, the bunch of them should settle down and be getting along just fine. The key is not to rush things, and to give both sides a lot of individual attention in the interim. In no time at all, your kitten will be part of your clowder of cats.