The Publication Manual bases its standard for citing court decisions on the Bluebook Rule 10.
Cite the name of the case (italicized) and the year of the decision.
(Harper v. Virginia Board of Elections, 1966)
Harper v. Virginia Board of Elections. 383 U.S. 663. Supreme Court of the United States. 1966.
Supreme Court decisions are published in United States Reports, abbreviated "U.S." 383 U.S. 663 refers to volume 383 of United States Reports, page 663.
For additional examples, and other types of courts, see pages 217-219 of the Publication Manual of the American Psychological Association (2010).