First off you will have to get from the car to the office so polite leash manners are a must. Once in the office they should also be under control. A sit stay or down stay is helpful while you are waiting to see the Dr.,paying your bill or being weighed on the scale. No flexi leads! Your dog should not be zinging through the office. Teaching the dog to settle in many places is key to having a calm dog in the vets office.
While you are waiting out in the lobby you can have your dog settle on his mat and chew on a Kong or other yummy chewy. This will help relax him and give him something to do so he is less anxious. Bring treats and do a training session as a way to channel any nervous energy and create a more positive association with the vets office.
When being examined by the vet it is helpful they stand still for the exam. Teaching your dog that gentle restraint is ok before taking them to someplace scary is key. Body handling like touching paws, mouth, ears, belly, and tail are all part of being examined. If your dog has a tendency to become aggressive you can acclimate him to wearing a muzzle. If you put the dogs teeth away everyone in the room seems to relax and the exam goes much smoother.
You can get nylon muzzles or basket muzzles at the pet store. Use squeeze cheese and let the dog have a lick if they put their face in the muzzle. Pretty soon your dog will be shoving his nose into the muzzle happily to get a lick of cheese. Keep the association happy. Randomly put the muzzle on so they get to wear it in all kinds of situations not just when something uncomfortable is going to happen.
It is proper etiquette to let the veterinary staff restrain your dog for the exam and any procedures the vet performs in the exam room. Safety is their main concern and if anyone gets bit then the veterinarian can be held liable. Calmly let the staff take control of your dog and stand back out of the way. If you are calm and matter of fact about what is going on then your dog will be more relaxed. All of the work you do with your dog prior to the vet visit pays off now while your dog is being still and calm while the staff handles the dog.
Many times the staff will take the dog out of the exam room to the treatment area to perform a quick procedure. Your dog most likely will handle this fine and they usually relax with the staff and not have to worry about your emotional state during the procedure. Things like nail trims and blood draws can happen quickly and efficiently with a vet and the staff working together with the owner out of the way.
After the visit you will need to pay for services. If your dog can't be trusted to wait calmly with you while you write a check take them out to the car and come back inside to pay. Some vets have a place you can tie you dog while you pay so you don't have to hold the leash. If your dog can be tethered and not pull or lunge at other dogs this is a great option.
When trying to find the right vet ask your dog friends who they recommend. If you are comfortable with talking with the staff and the Dr. chances are you will have a good experience with that vet. If you have special concerns with your dogs behavior during vet visits you can ask them how they will handle it. Many vets can also refer you to a professional trainer to help you work through some of the issues.