Always follow your veterinarians advice about feeding after your dog has had dental surgery. If your dog won't eat immediately after his dental surgery it's not really something to be concerned about. Dental surgery for dogs is basically a very aggressive version of a human teeth cleaning combined with the side-effects of anesthesia (often, nausea).
A 24-36 hour fast won't hurt your dog, but if your dog goes more than a day without food they may be experiencing pain chewing and you may need to help them begin eating by feeding something other than crunchy kibble. To get your dog to eat after dental surgery you can either soak his food in warm water or low sodium broth for 10-15 minutes to make a warm mush that doesn't need much chewing, or water down canned dog food with water or low sodium broth to make a slurry. As your dog heals you can soak the dog food for less and less time until your dog is weaned back onto solid dog food again. If your dog won't eat after surgery and continues this behavior you absolutely need to contact your vet, as there could have been additional trauma to his teeth or jaw during the cleaning that's causing him not to eat.
Despite what you may have been told, annual dental cleanings are not standard for dogs. Many holistic veterinarians argue that cleaning teeth annually can actually have more negative effects than positive! Anesthesia is difficult for a dog's system and there is nothing done during this expensive procedure that cannot be accomplished with changes to the way you feed or treat your dog.
According to the American Veterinary Dental Society, more than 80% of dogs suffer from periodontal disease by the age of two. Help your dog ward off bad breath, gum disease, multiple infections, and heart disease by consistently brushing your dog's teeth or using a tooth cleaning toy.