The most common way for a case to reach the Supreme Court is on appeal from a circuit court. A party seeking to appeal a decision of a circuit court can file a petition to the Supreme Court for a writ of certiorari. "Certiorari" is a Latin word meaning "to inform", in the sense that the petition informs the Court of the request for review.
Unlike all other federal courts, the Supreme Court has discretion to decide which cases it will hear. The Supreme Court gets thousands of petitions for certiorari, but only issues a writ in a fraction of cases. The Court will only issue a writ if four of the nine Justices vote to do so. Justices usually take the importance of a given case and the need to issue a final decision before deciding to grant certiorari. If four Justices do not agree to grant certiorari, the petition is denied. If a case is "denied cert", the decision of the lower court is final.
Another way in which a case can reach the Supreme Court is through an appeal from a state supreme court. Each state has its own supreme court that is the final authority on state law.
