The correct way to cite a Supreme Court case is: Petitioner v. Respondent, Volume Series Page (Year), like this: Plessy v. Ferguson, 163 U.S. 537 (1896).
When a new case is made public, they print up an official copy of the opinion(s) (including concurring and dissenting views) called a “slip opinion”. From a slip opinion, you can give a half-way decent legal cite, as follows: Alexander v. Sandoval 532 U.S. __ (2001).
In this example, “Alexander” is the name of the Petitioner, or if there is more than one, the first one listed. “Sandoval” is the Respondent. Petitioner is not necessarily the plaintiff, the person who filed the original complaint. In fact, in this case, Sandoval was the plaintiff. The petitioner is just the party who lost in the Federal Court of Appeals, and is now seeking review by the Supreme Court. You could say “appellant”, but you’d be wrong. The procedure for getting into the Supreme Court is not by appeal, it’s by petition for writ of certiorari, hence “petitioner”.
Now, how do I expect non-lawyers to know that? I don’t. If you have a slip opinion, you don’t have to: the correct names of the parties are printed at the top of every even-numbered page.
Now that I’ve exposed that deep dark secret, I might as well risk disbarrment by revealing that the correct cite appears at the top of every odd-numbered page. It says: “Cite as: 532 U.S. __ (2001)”.
What does it mean? Standard legal citation follows the format: Volume Series Page. It means that this opinion was decided in the year 2001 and that, when it finally gets printed in a big, fat law book, it will be in Volume 532 of the United States Reports (cited “U.S.”). When the Reporter of Opinions printed this Slip Opinion, they did not know what page it was going to appear on, so they left a blank.
Eventually, your case will be printed in no less than three widely-used series: United States Reports (the official one) (“U.S.”), West Publishing’s Supreme Court Reporter (“S.Ct.”) and the Lawyer’s Cooperative Edition, Second Series (“L.Ed.2d”). The full correct citation would be: Alexander v. Sandoval, 532 U.S. 275, 121 S.Ct. 1511, 149 L.Ed.2d 517 (2001). This is essential for law review, but too pedantic for E2. The other two series cross-reference the official “U.S.” series, so the official, “U.S.” citation is sufficient to pinpoint any quote you want to make.