Use Google Scholar to find full-text legal opinions from the U.S. federal and state district, appellate and supreme courts. For more information, see Finding the laws that govern us (Google blog).
Federal Case Materials Checklist
How to Find a Case by Name or Topic Using Print Sources
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Understanding the Federal Courts
This 54-page publication (in PDF) provides an introduction to the federal judicial system, its organization and administration, and its relationship to the legislative and executive branches of the government. Published by the Administrative Office of the U.S. Courts in 2003.
Please note that U.S. District Court cases are not as readily available for free on the Internet (except for those opinions posted on the courts' official Web sites, which are typically only the most recent decisions, and through Justia).