When you get a new cat, you should always remember if you have a resident cat or cats, they do have feelings, and it is important to respect them. Additionally, any new addition should be kept in isolation for at least a few days to be sure they didn't bring home any sickness (we isolate most new cats for 4 weeks, but since we have young kittens often, we have to take more precautions than the average owner.)
First, before you bring home your new cat/kitten, decide where they will live their first few days. Pick a room that is NOT frequented by your current cats very often. For example: a spare bathroom, a utility room, or a spare bedroom. If your current cat sleeps every night with you, putting the new cat/kitten in the bedroom with you is the worst place possible. You will upset your current cat(s) and possibly end up with some "presents" left in places other than the litter box.
Have the litter box, food, and water prepared before your bring home the new cat/kitten. Find out what kind of food the breeder (or previous owner) has been using so you can have that on hand to make the transition easy. If you want to switch foods to whatever food you use, do so slowly.
When you bring home the new cat/kitten, carry it in the carrier all the way to the new room. While you may be tempted to pull it out and shove it in the face(s) of your current cat(s), resist this temptation. Put the cat/kitten in the carrier in the new room. Open the carrier and let the new cat/kitten come out on their own time. If the cat/kitten seems very upset, leave the room and let them have some quiet. If they are out quickly and wanting affection, give them some affection, then leave the room and give your current cat(s) lots of extra love to remind them you still love them.
For the next few days, keep the door closed. Let the new cat/kitten and the current cat(s) smell each other under the door. Watch your current cat(s) for signs of stress. During this time, take the new cat/kitten for a wellness check to your vet (as well as a test for FeLeuk/FIV. Any new feline member should be tested for these two diseases before being allowed to be with your other cats). If everything checks out and all the cats involved seem to be ready to meet, open the door a little and let the new cat/kitten explore the house from that room. If a fight happens, take the new cat/kitten back to the room for a few more days. A little hissing is ok, but a full-blown fight is not.
Hopefully, the new cat/kitten and the current cat(s) will quickly integrate into a happy household and you will be a happy owner of more than one cat!