Many shelters offer free pet adoption promotions. During these limited-time events, the adoption fee is waived and the dog can be adopted for free. Some private adoptions also offer dogs for free.
Some people may qualify for special free adoptions as well. Many shelters and organizations offer "Seniors for Seniors" programs that provide free pets for elderly people. Some also work with low-income or special needs families to place dogs for free. The best way to find programs like this is to simply call local shelters and ask about them, although some are listed on websites as well.
Private adoptions are another possibility but they are riskier and may cost more in the long run. These dogs may be available for free but there is no temperament testing done. The dog may have health problems or require veterinary care, such as vaccinations or spaying or neutering, while a free shelter dog generally already has these procedures done. Shelters also often provide additional support, such as free or low-cost training, and they can take the dog back if the adoption does not work out.
All new dog owners still need to plan for the cost of buying equipment and food for their new pets. A waived adoption fee can help with that, but these costs are unavoidable.