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.