How do I get my cat used to the carrier without stressing it out?

The key is getting him used to it gradually, keeping the carrier always accessible around the house like it's just a normal spot. Leave it open, put a soft blanket or a toy that smells like him inside, maybe some treats too. The cat needs to associate it with something positive, not "okay, now you're going to the vet."

Start with super short sessions: does he go in on his own? Give him a reward. Then close the door for just a few seconds while he's inside and calm, then open it right back up. Increase the time little by little, no rush. Some cats get there in days, others in weeks, but there's no point forcing it.

When you actually need to use it for a trip, don't make a big deal about it beforehand: stay calm, put him in naturally. If the cat picks up on your anxiety, he'll get even more stressed. During the ride, talk to him in a calm, soothing voice. There are also pheromone sprays you can spray inside the carrier that help a lot - look for ones with feline pheromones.