Is your cat aggressive or skittish now? What is his/her temperament?
You definitely need a cat carrier, preferable one with a top load as well as a front load. Line it with a comfy blanket or towel. If your cat is combative, you may need help getting him/her into the carrier.
At the vet itself...honestly, most cats are FINE. I'm amazed at the treatments and procedures that my cats have tolerated VERY well at the vet's. I think they just know that this is for their benefit, plus the vet and vet techs do a great job of knowing how to handle a cat. NEVER an issue. I was even amazed at how easily one of my cats got back IN to the carrier (he was a problem getting in to it) until a vet tech told me "they are always better when they know they are going HOME."

Yeah, I think he's right.
Honestly, I wouldn't worry about it, the vets know what to do. Just be sure you have your side ready with the right kind of carrier and making the whole experience of transporting as stress-free as possible for your cat. Good luck!