The Supreme Court makes national policies. National policies are those which affect the whole nation.
The Supreme Court controls which cases it hears (its docket) and hears less than 100 annually. Most of this docket is cases on appeal from lower courts or state courts, but there are still some cases that are part of the Court's original Constitutional jurisdiction. Cases usually reach the Supreme Court after all other avenues have been exhausted, and these cases must concern a substantial federal question.
Justices may have agreeing votes on a case, but their legals reasons may be different. Both the Supreme Court's decision and the reasoning are both very important.
A justice may support a decision but not the reasoning and thus change his or her vote. When discussing a case in private, justices often try to win support of their fellow justices. Also, judges may try to influence their fellows in how their opinions are written. In addition, judges may try to influence selection of Court personnel.
The founders disagreed on how to structure a federal judiciary, establishing only a single Supreme Court.
At the Constitutional Convention, those who opposed the creation of national courts believed that federal courts would usurp the authority of state courts. The rest of the system was left to Congress, and the Judiciary Act of 1789 finalized a system of district courts, circuit courts and the Supreme Court. Chief Justice John Marshall developed the Supreme Court into a branch of government that used judicial review to check the executive and legislative branches. The Marbury v. Madison case established judicial review as the Supreme Court exclusive authority to determine the meaning of the Constitution.
The Supreme Court is in session from October until June or July. Justices decide which cases to hear mainly via a Writ of Certiorari (Sur-Shuh-Rory).
A Writ of Certiorari requires agreement of four of nine justices to hear the case. Cases usually heard involve: two (or more) lower courts disagreeing; lower courts conflicting with Supreme Court rulings; questions of broad constitutional significance; urging of the Solicitor General. Agreeing to hear a case does not denote agreement on the case itself.
Once justices agree to hear a case, oral arguments are scheduled. Participants get equal amounts of time -- usually one hour. Justices then read legal briefs (arguments) from all parties in the case. These briefs include those from the plantiff, defendent and any amicus briefs. Afterward, the justices meet in conference to privately discuss issues involved in each case. The Chief Justice selects one person to write the official court decision and opinion.
There are three types of decisions:
Court can affirm the decision of the lower court;
Court can reverse the decision of the lower court;
Court can remand the case to its original court.