A writ of certiorari must be presented for a case to be heard at a higher level. Generally it goes from county, circuit, District Courts of Appeal, and then Supreme court.
The U.S. court system, like other court systems, uses common law
. This basically dictates that any ruling made on a case will be used in the future to determine future cases (thus giving it power). Any order made by the court is *usually* going to be done. This does not always happen, as evident by Brown v. Board of Education
. The northern schools integrated at a much faster pace than the southern schools.
The Supreme Court rules on whatever they choose to bring up. Since thousands of appeals are sent their way, they have the authority to choose which cases to consider.