It is much easier bringing home a domestic cat then a feral as they are usually fine with people. Though some cats will still be shy or skittish in the first couple of weeks while they settle and get to know you - time, patience and love is what they need.
Arrival of the new cat
Kittens are very adaptable, excitable and curious so just being left to explore may be enough. Just remember to show them where the toilet (which should be a indoor litter tray) and their food and water are. If the kitten is more nervous they should be coaxed to explore and interact with you until they are comfortable.
As with the kittens if the cat is adventurous being left to explore while being shown were the food, water and litter is may be enough to settle them. If the cat appears nervous keep the environment quite and leave them to settle. If the cat is distressed a small area should be made for them with everything they need where they can calm down.
After the cat has been in the house for a couple of hours (or when they appear to settle) slowly approach them and either crouch or lay down and slowly offer a hand for them to sniff. Talk to them in a soothing voice from a distance if they are nervous of you - leaving them alone if necessary. After you have made successful introductions with the cat spending time with them grooming, playing and just being with each other is the best way to continue bonding.
The Great Outdoors
It is advised to keep your new cat inside for at least 3 weeks while they adjust to their new home. This is to stop them trying to get back to their old owner, shelter, etc.
The Horror of the Vacuum
Hoovers are loud and startle most cats - make sure all the hoovering is done before the cat arrives and avoid doing anymore for a couple of days while the cat settles.