The below text is excerpted on page 5 from Measuring America: The Decennial Censuses From 1790 to 2000.
The early census acts prescribed the inquiries in each decennial census, but the U.S. Government did not furnish uniform printed schedules until 1830. In 1790, the marshals submitted their returns in whatever form they found convenient (and sometimes with added information).In 1790, marshals took the census in the original 13 states; plus the districts of Kentucky, Maine, and Vermont; and the Southwest Territory (Tennessee). Each household provided the name of the head of the family and the number of persons in each household of the following descriptions: Free White males of 16 years and upward (to assess the countries industrial and military potential), free White males under 16 years, free White females, all other free persons (by sex and color), and slaves.
U.S. marshals conducted the 1790 census following instructions found in "An Act providing for the enumeration of the Inhabitants of the United States," from March 1, 1790.