1795 Naturalization Act (An act to establish an uniform rule of naturalization, and to repeal the act heretofore passed on that subject)
Sess. II, Chap. 19, 20; 1 stat 414.
3rd Congress; January 29, 1795.
Any free white person could recieve citizenship providing they had renounced their allegiance to their previous state/sovereignty by name, lived in the United States for five years at least, behave as a man of good moral character, and renounced any title they possessed in the previous states. Once the applicant had been approved and recorded by the court clerk, all related children would receive citizenship whether they had been born in or outside the U.S. providing their father had at some point, resided in the U.S., and never been legally convicted of joining the army of Great Britain.
(Summary by Shelby Englund)
Background History of the United States Naturalization Process - This site provides a collective overview of the history of naturalization starting with the 1790 law.
Naturalization and Citizenship: Nature and Scope of Congress' Power - This site provides an annotated version of the U.S. Constitution, here focusing on naturalization law.
Naturalization Records (from the National Archives) - This site is helpful to show the transitions of naturalization law starting in 1790.