To find case law of the Supreme Court, you should start at the United States Supreme Court Digest - Table of Cases. This will point you to the right volume of the Supreme Court Reporter series, which number in the hundreds of volumes.
There are two indexes to the US Supreme Court Digest:
Let's say we are looking for: Miranda v. Arizona (a 1966 case, which established the right to remain silent and to consult an attorney during police custody & interrogation).
Since it starts with M, this would be Volume 15 of the Table of Cases index...
Cases are listed alphabetically, so we flip the pages over to the M section ...
We're looking for the Supreme Court Reporter (abbreviated: S.Ct.) in this entry. 86 is the volume, SCt is the reporter, and 1602 is the starting page for this case. See image, below..
Next, we go to the Supreme Court Reporter (abbreviated: S. Ct.), find volume 86 (notice there are two volumes numbered 86 here. Look at the page number range they each cover. We are looking for page 1602). Finally, turn to page 1602. And, there it is!