Today is the international Take your cat to the vet day! Unfortunately, little fuzzball doesn’t care about human days. What shall you do?
Start with doing mock checkups at home, to get the kitty used to being poked, prodded and squeezed. Get the cat familiarized with the (preferably) solid carrier let Admiral Wuss-Wuss sleep in it, leave in the living room, and make it a general part of life. Next comes car familiarization: take your cat on small rides, and gently increase their length so that Mittens gets used to it, as well as disassociating rides from vet visits.
Its also a good thing to take a towel or blanket that smells of home with you. Use it to make the kitty calmer in the waiting room, in the procedure area, and even leave this bit of home if overnight stay is required. Having a good rapport with the vet also helps being less stressed and having a caring doctor helps the cat, too!