Final answer:
Cases are selected for the Supreme Court based on a request for judicial review called a writ of certiorari. The Court only takes cases that involve a constitutional question or differing interpretations of a law. Four out of nine justices must agree for certiorari to be granted.
Step-by-step explanation:
Almost all cases come to the Supreme Court on appeal from another, lower court such as the US Court of Appeals or a state Supreme Court. Most cases are selected to be heard based on a writ of certiorari, which is a request for judicial review and an order directing the lower court to send its records to the Supreme Court for review. Either of the sides in the case can petition for the writ, but few will actually be granted - the Court only takes those cases in which there is a constitutional question or there have been differing interpretations of a law. The lower court's decision stands if certiorari is not granted - often this is because the justices believe the correct decision was made by the lower court or that there is no significant legal question to be addressed. Four of the nine justices must agree in order for certiorari to be granted.