Take a good sturdy carrier box with you to collect your new cat to make sure he doesn't escape on the journey home.
If you are getting a kitten, it is a good idea to take a piece of cloth or bedding from the breeders home with you so that the scent of his home is still there. Alternatively, you could use Feliway spray in the box to help calm the cat down.
Try to make sure that your journey is as short as possible. It is a good idea to have your new cat checked over by your own vet on the way home so that if something is wrong, you are not too attached to it! Other than this stop, take your cat straight home.
Before leaving the breeder or rescue centre, make sure that all relevant paperwork is filled in. Do not agree to having anything sent on to you, make sure that all relevant documents are present before you take your cat home. This is particularly relevant to pedigree papers.
Take a sample of the food that the cat has been receiving so that you can continue to feed this for the first few days.
If you have any other pets, keep them out of the way while the newcomer is exploring their new surroundings. Open the cat box in an enclosed, quiet room and allow them to come out in their own time. Having a Feliway diffuser in the room can help the cat feel more confident. Do not offer them food immediately as this may cause an upset stomach. Do provide a litter tray though.
Allow the cat to explore each room of the house in turn. Do not try to fuss them but if they come to you, feel free to give them a stroke. Playing with kittens can help them to settle in but do not be too rough. It is usually best to keep young children out of the way while the cat/kitten is exploring.
Once the cat seems fairly settled, the introductions to the rest of the family can take place. Try to keep the situation as calm as possible. I will deal with introducing a new cat to existing animals elsewhere.