The most important first step is to make sure your dog has the right vaccination, especially rabies, which is mandatory and must be administered annually. Cats are expected to have panlucopinia vaccines for feline leukemia. Both dogs and cats should be further treated for parasites. Once again, we suggest you check with the relevant embassy or consulate involved before leaving the country. They will give you the exact paperwork requirements which you will need to fulfill.
Similar principles apply on exiting as on entering.
You'll need a certificate of vaccination against rabies, and also a certificate of health signed and sealed by a veterinarian five to ten days before your departure from Mexico. Before departing from the country you will have to check in to S.A.G.A.R. which will give you the necessary export license to leave the country after a brief visual inspection of your dog. There will be no cost for this license for up to two dogs or cats. There is a choice of veterinarians in Mexico and they do make house calls. They will be the ones to contact for anything relating to your pet's health, and also the ones to administer the necessary vaccines.