You can find free or inexpensive vaccination clinics by contacting local animal shelters or your city's animal welfare department. Most puppy vaccines are available at a low cost rather than for free, although some clinics provide rabies vaccinations for free.
Some pet supply stores and vet clinics also offer low-cost shot clinics, especially larger chain stores such as Tractor Supply Company. There are also private funds and charities in most states that offer financial assistance for veterinary bills and may be able to pay for your puppy's shots. The Humane Society of the United States provides a list of larger organizations, or your local animal shelters may be able to help you find assistance.
Most shot clinics offer sliding-scale payments or a fixed low-cost payment. Many vaccinations are available for under $10.