The best way to save money on vet bills is...not to have any vet bills! right? There are several things you can do to keep your pet healthy without the intervention of a vet.
Spay & Neuter
This one item alone will help keep your pet from wandering as well as overpopulating the planet with more "unwanted" pets. Like people, pets carry harmful viruses that are transmitted when pets are allowed to roam freely.
There are a number of required vaccines which your pet should be kept up to date on. These include things such as Parvo and Feline Leukemia, rabies and distemper. Without these immunizations, your pet could cost you a whole lot more than what you have budgeted for their care.
Food & Exercise
Don't just feed your pet so you can say "I fed the pet!" There are good pet foods as well as poor quality pet foods. It's best that you buy the best quality you can for your animals. Nutrition is far more than healthy teeth and a shiny coat.
Every animal needs to get their blood circulating on occasion. Take your dog for a walk. If there's a dog park close by...all the better. Cats present a different situation. Some felines can be trained to a harness and leash but most prefer to play inside on a climbing tree...with attached toys. Either way, your animals need exercise just as much as you do. The better the circulation, the faster the body can rid itself of toxins.
The primary reason for keeping the gate to the yard closed is so Fido won't get loose or lost. Make certain that when your pet is turned out for the day that they have a safe haven from the hot sun or the pouring rain. See to it that they have access to fresh clean water. No animal would choose to drink from a slimy algae filled bucket with dead bugs floating across the top.
Be proactive so your vet won't have to be reactive...besides, being proactive is a whole lot cheaper in the long run.
If you find that your pet has an ongoing condition that does require the services of a veterinarian, there are several discounted vet hospitals around the country that you can locate in your local phone book or on the Internet.
There are also pet insurance agencies where owners co-op their funds for emergency services and procedures.
Some vets (although not many) give discounts to those who have all their animals seen at the same vet clinic/hospital.