Going to the vet can be a traumatizing experience for many cats but there are ways to lessen anxiety. Try to bring your cat to the vet in a carrier to make him/her feel more comfortable about travel. Cats like to be in enclosed spaces as it feels safe. Try to pick a carrier that is spacious and can be easily taken apart: look for one with a removable top or sides to make it easier to remove your cat from the carrier once you arrive at the vet.
Try to remain calm as pets can sense worry and frustration. Don’t chase your cat to get him/her in the carrier as it will likely just exacerbate fear. The best approach is to try to get your cat to come to you. You may consider leaving the carrier out in a common area of your house so your cat can familiarize him/herself with it. Sometimes putting a blanket or towel in the carrier can reduce your cat’s anxiety by surrounding him/her with familiar smells.