Remember that your veterinarian and his/her staff are there to help you and that you and your pet are their primary interest. Don't ever be afraid to ask questions.
Make sure you understand the name of the medication, what it was given for and the strength of the medication. These may seem like simple questions, but you never know if you may have to explain this on the phone to another hospital or your own veterinarian's office.
Ask if there are any common side effects. Is it given as needed or at certain times of the day? Is it given with food? Do you have to get up in the night to give it? What side effects are there (e.g. urinating a lot, drinking a lot of water)?
Specific disease or injury
Is exercise restriction involved? How strict? Can you let your dog out into the yard? Or do you have to restrict him to leash walks only? Is he to play with other animals? Should you confine him to a cage or crate? Will he need to be exercised more often?
Anything special you should know about at-home care? Can he eliminate on his own? Is there anything specific you should watch for?
Make sure to ask what the prognosis (outcome) is. Is it curable? Will it come back or can you prevent it (e.g., pancreatitis from too much "people food")?
Is there a special diet your pet has to follow? Can you get it at any pet store, make it at home (like a rice/ground beef mixture) or is it only available at your veterinarian's?
Is this disease or injury common in your pet's breed or size?
Other animals or people
Will other animals treat your pet differently because of the disease? Will he smell differently to them, so should you separate them?
Also make sure your veterinarian can be reached in the event of an emergency or that his staff tells you whom to call.