First, because it is not practical to quarantine a cat, take them to the vet for a health inspection to rule out any communicable diseases. You don’t want to risk giving your other animals a disease that could be prevented, and a health inspection is a good idea even if you don’t have other animals at home.
Second, remember to take your time. Start by isolating the new cat in a room by itself to help it get used to the new scents and sounds. Spend lots of time with the new cat, letting him get to know you and settle in before staging a meeting between cats.
If possible, when introducing the cats to each other, keep the new cat safely confined in a crate to allow the two to meet each other without risk of a fight. Let them meet this way, and then gradually begin introducing the new cat to the rest of the house.
Some fighting is not uncommon – all animals have a hierarchy that must be established, so the old cat and new must duke it out to see who is the leader. Just make sure the squabbles don’t get out of hand and be prepared to break up a fight if necessary.
Above all, be patient and take your time. This is a major change for everyone involved, and can be made more traumatic by forcing the issue.
Once your cats have had a chance to get to know each other, you can relax and enjoy watching the two become friends.