Calculus from under the gum tissue is carefully removed using a hand scaler. Finally, the teeth are polished to reduce purchase for new deposits. This can often be done when the dog is under anasthetic for other reasons, such as neutering. Cavities, etc Dogs do not commonly get cavities. When they do occur, it is more often at the root of the tooth rather than at the crown.
Cavities can lead to root abscesses.
Abscessed roots often cause a swelling just below the animal's eye. Generally, tooth extractions are needed at this point.