A brief is a written legal document that is presented to the court arguing why a party to the case should have a decision in their favor.
Headnotes are summaries of the key legal points. Headnotes are useful for a quick understanding of the decision, but they are the editor's remarks and not the court's. Footnotes, however, are written by the justices on the court.
An Opinion is an explanation of the decision of the court. In the Supreme Court opinions are catagorized thus:
A syllabus summarizes the points decided in the case.
Background: (available online)
1) Hemmens, C., Del Carmen, R., & Brody, D. (2010). Criminal procedure and the Supreme Court a guide to the major decisions on search and seizure, privacy, and individual rights. Lanham, Md.: Rowman & Littlefield.
* A reference book for federal officers, this book focuses on criminal procedure rights and the case law associated with them.
To find the actual opinions of the court cases you will be reading, there are lots of online resources. For background on the cases and links to the opinion I prefer Oyez because it is easier to use, and doesn't have adds.
Use the search box at the top of the screen to search for individual cases:
Find your case in the list:
After you click you'll see information about the case, as well as a link to the Opinion (click on View Case)
If you want to look up more in depth background information about Supreme Court cases, here are a few books:
Levy, L. W. (2000). Encyclopedia of the American constitution. 2nd ed. / New York: Macmillan Reference USA. http://www.galileo.usg.edu/express?link=enc2-uga1
Savage, D. G. (2009). The Supreme Court and the powers of the American government (2nd ed.). Washington, DC: Congressional Quarterly Press. http://galileo-usg-uga-primo.hosted.exlibrisgroup.com/UGA:UGA:01GALI_USG_ALMA7111620904000293