For cats, low-stress visits to the vet start at home.
Thankfully, there are many things that can help before you leave the house. Choose a cat carrier that has multiple access points of doors on the front and top of the carrier. Also, look for one that is easy to take apart and has quick-release latches instead of screws.
Leave the carrier somewhere in your home that your cat likes to spend time in it and it will become a safe space. The next time you put them in it to go to the vet, they will be more comfortable and familiar with the carrier.
Lastly, cats prefer to remain out of sight, so draping a towel over the carrier, or better yet, a towel sprayed with Feliway pheromone can significantly reduce stress levels.