Information provided here comes from medicalantiques.com, Science magazine, and a number of academic studies including
Rothstein, William G. 1972. American Physicians in the Nineteenth Century. From Sects to Science. Johns Hopkins University Press.
Before about 1750 most men aspiring to become a doctor generally did so by apprenticing themselves to an already established physician. Those who could afford a more formal education studied in Europe.
In the mid-1700s the first medical schools were established in the U.S. Columbia University in the City of New York opened its medical school in 1767, the University of Pennsylvania in 1769 and Harvard University in 1783. Apprenticeship was still a common approach to practicing medicine, lasting around three years.
With advances in science and technology medical school curricula became more rigorous, and more schools were opened.