When we get new cats, whether planned or by rescuing them, we have a responsibility to the new cats to care for them, and to our existing kitties so that they know they are not being replaced.
Once these responsibilities are met, and the new cats are calmed down, comfortable and on a similar schedule, then introductions can be made. One nose at a time to another nose. Supervised only, and with protection for each cat. This should be done in neutral territory - not near food bowls or litter boxes. Once kitties have started growling and hissing, separate them and give everyone some time out to calm down. Repeat as necessary.
If a new cat is feral and the existing cats are not, then you have a duty to tame that cat or release it. It should be spayed or neutered before release. If you choose to tame it, I suggest you come to the website for details on how to tame a feral cat. That will ensure that your new cat learns to trust humans and won't try to eat your budgie or your house plants.
Our existing kitties will best be served by play sessions. These let our cats know that we love and value them. I suggest a good, rousing play session of at least 15 minutes, twice a day. Use toys on strings. sticks, or balls. Once your bond is renewed, you can also use the play therapy to help the cats adjust to each other. Play therapy is the best technique to help cats bond.
Give your cat some catnip. However, do not give catnip to your combined kitty family for at least a week or two after introductions. They need to learn to trust each other before you introduce that element. So, use play therapy for two weeks, then sprinkle catnip around for them. The bonds should be cemented after that.