Final answer:
Cases reach the Supreme Court through appeals from lower courts. The Court selects cases based on a writ of certiorari, which is a request for judicial review. The justices make their decision based on briefs, records of lower courts, and amicus curiae briefs.
Step-by-step explanation:
Most cases reach the Supreme Court on appeal from another lower court, such as the US Court of Appeals or a state Supreme Court. They are selected to be heard based on a request for judicial review called a writ of certiorari. Both sides in the case can petition for the writ, but only a few are granted. The Court takes cases that involve a constitutional question or have differing interpretations of a law. If certiorari is not granted, the lower court's decision stands.
Once a case is accepted, the attorneys prepare and submit briefs presenting arguments and relevant precedents. The justices base their decisions on these briefs and the records of the lower courts. The Court also considers amicus curiae briefs submitted by groups with an interest in the case. After oral arguments, the justices vote on the case in a private conference, and a majority decision is reached. Finally, the Court announces its decision to the public.