Contact your local animal shelter or rescue organizations to ask about free and low-cost veterinary care. These organizations sometimes provide free routine care, such as vaccinations and spay or neuter surgery.
Consider buying pet health insurance. Although this is not technically free since you have to pay a premium every month, it can offset the cost of emergency surgery or other large veterinary bills. You can also talk to your veterinarian to see if you can work off some or all of the payment by doing work around the clinic, such as working as a receptionist or cleaning the facility.
Try asking rescues about veterinary funds. These funds are typically designed to help with emergency veterinary bills. Some funds focus on specific breeds or species, while some are more general. Your vet still gets paid, but the money comes from the fund.
If none of these options work, see if you can work out an affordable payment plan. Some veterinarians are willing to take payments from regular clients. Look into CareCredit.com, which offers a special line of credit designed for veterinary and health expenses. As long as your veterinarian accepts it, you can use it to pay for virtually anything, including routine procedures and emergency treatment. There are a variety of low- and no-interest plans to help you minimize the expense.