Any tips for introducing a new cat to my apartment?

Get the vet's aftercare instructions from the current owner. Bring the carrier in and set it on the floor in a place where the cat can see you fairly often. In the living room beside the sofa, for instance. Go about your usual activities for an hour or so. Then open the door of the carrier and let the cat come out when he feels like it. Put a bowl of water outside the carrier. Don't worry about food right away. Make sure the litter box is somewhere easily accessible. Put a water bowl wherever you plan to always have one. Put a food bowl there too, and you can put food in it later that day if you like but don't be surprised if the cat doesn't eat for a day or so. Once the cat comes out of the carrier, speak to him, but don't try to pet him or pick him up. Let him explore or hide or whatever he wants to do. He'll approach you when he's ready, when he feels comfortable in the new place. It's not unusual for cats in new places to hide under the bed for a few days. I had one who stayed in the basement for a week.

A bed in a safe quiet place, water for it and a litter try to come around from its anesthitic

put your cat in a small, quiet room by himself if possible....put litter box on one side-food and water on other side...open door to crate and let him explore if he wants. he may just want to hide--cats will hide in a new territory until they feel safe. do not run after your cat trying to get him to cuddle-he is in overload-surgery and a new territory! eek! so keep it all nice and calm and let him come to you when he is ready. do not panic if he doesn't eat or poop for the first few days (nothing in-nothing out) he has to learn to trust his new environment-so give him time. later on you can move food bowl, water and litter to their permanent spots.