Veterinary is almost essential if you plan to use pets very much. Skilled veterinarians can heal pets quickly and efficiently, and can even resurrect dead pets if they are bonded.
To use the veterinary skill, simply use bandages on an animal. The easiest way is to use the [band in-game command. Note that with the veterinary skill you can bandage wild animals and even enemies. For maximum effect when bandaging animals, you also need the animal lore skill.
In addition to bandages, pets can also be healed with magical means such as the magery or chivalry cure and heal spells. Use both simultaneously for fast healing.
Not only does increased skill give your bandages more effect on pets, it also provides you more stable slots at animal trainers.
Train the veterinary skill by bandaging your pets; no complex strategy necessary.