You should plan on doing a gradual introduction between the kitties by starting them off in separate rooms (a bathroom is fine). See how they react to the "stranger behind the door". If they're hissy or growly, then leave the door closed between them a few days. If they're curious or crying to get through, then prop the door open an inch (a book and a doorstop can work for this).

See how your pre-resident cat(s) react to seeing the strange cat. If they're curious rather than aggressive, then put the new cat in a carrier and bring him/her out into the larger room. Is there hostile behavior like growling, hissing, spitting, or attacks? Then take a break and return the kitty into their separate space, and try repeating the exercise again later, with enough iterations that it becomes a non-event.

Once the in-carrier visits are calm, then have a blanket ready in case of problems, and try opening the carrier door. This is an important point to get your pre-existing kitties involved in their favorite activities and for you to act as if you are completely ignoring the newcomer, to re-assure your "old" cat(s) that they're not being replaced. Don't give the new kitty any attention until the other felines have accepted the newcomer themselves. Wait until the newbie is sequestered again behind a closed door before attending it.

If there is heavy staring, stalking, growling, swatting, or an actual fight, then make a sudden loud noise (hand-clap, yell "hey", hiss, foot-stamp, slap-a-wall) to separate and distract the cats and cover one (preferably the aggressor) with a blanket, towel, or inverted laundry basket. Remove the covered kitty to a small room for at least 10 minutes.

Avoid directly picking up an aggressive or defensive cat because they might inadvertently defend themselves against you, and you're probably not covered by fur to protect your skin from scratches and bites. That's why the comforter or towel to swaddle the kitty.

The best way to punish a cat to discourage misbehavior like aggression is a time-out in a small room like a bathroom. Cats hate losing their freedom and will quickly learn to avoid whatever occured before that loss. You can do this calmly - no additional negative re-inforcement is needed - although some repetition is likely necessary. Physical punishment normally does NOT work with cats and is never recommended.

Some folks suggest using a water pistol or spray bottle, but this can upset the cats further and heighten the aggression. It also isn't effective if it's NOT done in a clandestine manner to make the cats think their own actions is getting them wet. They assume that the psycho human just sprays them with water at random moments for no reason. It can damage their relationship with and trust of you.

The timeout room gives them a chance to calm down and relax. If 10 minutes doesn't return a calmer cat, try 20. Just make sure there's a water dish in the isolation room. Food and litter are good to have there as well if you can manage it.

It's quite likely with these very social creatures that little of the above is necessary, but it's best to be prepared.