Please remember that this is probably your kitten's first time away from the only home she has ever known. Give the kitten time and don't expect him to be best friends with you right away. Keep the kitten's introduction to other family members and pets as quiet and stress-free as possible and, most of all, allow him a day to become used to the new surroundings.
Show the kitten her litter box, food and water as soon as you get her home but be prepared for accidents! However, don't spank the baby if she misses her litter box! Rather, pick him up, put her in her box, and make digging motions with her front paws. Young kittens sometimes forget where their boxes are, or suddenly realize they have to go now - this is normal, and will pass quickly. Also, kittens do best with their 'own' litter box and their 'own' food bowl.
Introduce the kitten to one room at a time; offer encouragement and petting, but allow him to explore in his own time. After he is comfortable and settled down in the first room, allow him to proceed to others. Try not to startle the kitten, and again, remember that this is a stressful time. It is not unusual for a new kitten to hide, be skittish, or refuse to eat for a couple of days. Give lots of 'gentle' petting, soft speech, and encouragement and you will find that the kitten will quickly adjust.
Be aware that the kitten might cry a lot the first couple of nights. Although she is completely weaned, she may miss being around other cats or her mother, or just feel insecure and lonely. As soon as she makes friends with you and your other pet(s), this crying should stop. If the kitten does not stop crying, there could be another problem and you should consider consulting your vet.
Other Pets: If you have other pets, wait until the kitten is settled and comfortable before bringing in other animals, then only one at a time. Do not leave the kitten alone with the other pet(s) until you are certain that they are good friends (this may be several weeks!). First let the animals smell where the other has been and then see each other from a distance. When they are first introduced, if they are a dog and cat, have the dog on a leash and make sure the cat does not scratch the dog (keep a water spray bottle handy). Be certain to give the pets already in your home lots of attention in order to prevent jealousy and avoid stirring territorial instincts. The original pet may not take too kindly to the new addition. The new kitten should have his own litter pan and food dish.