One method of finding free shih tzu puppies is to check the local Craigslist site or the classified section of a newspaper. Many people list puppies as "free to a good home" when their adult dogs have unexpected puppies.
Another way to find a free, or very inexpensive, shih tzu puppy is to check with a local rescue organization that focuses on shih tzus. Many dog rescues are not focused on making a profit and ask only for a donation to cover the costs of caring for the dog.
Be wary of puppies that come from a puppy mill, as these dogs are usually abused and forced to have puppies continuously throughout their lives.