Final answer:
The Supreme Court guides lower courts by setting precedent through its decisions, which lower courts must follow. The Supreme Court's authority is leveraged by interpreting the Constitution and reviewing significant cases via the writ of certiorari. It operates at the top of the federal judiciary system, which is structured across three tiers, including Circuit and District Courts.
Step-by-step explanation:
The Supreme Court is the highest judicial body in the United States and plays a crucial role in the federal judiciary system by setting precedents that guide lower courts. These include both federal and state courts. The judicial branch, as established by the Constitution, includes the Supreme Court and the lower courts created by Congress. Through its decisions, the Supreme Court interprets the Constitution and sets legal standards that lower courts must follow. This is done through the process of judicial review, primarily through the issuance of a writ of certiorari.
The federal court system is hierarchical and three-tiered, with the Supreme Court at the top, followed by Circuit Courts, and then District Courts at the base. Justices of the Supreme Court, including one chief justice and eight associate justices, are appointed for life, ensuring their independence. With only nine justices, the Supreme Court reviews cases that have constitutional significance, or where there has been a dispute regarding the interpretation of laws amongst lower courts. Its decisions are final and binding on all other courts.
Lastly, the structure of the federal judiciary and the lifetime appointment of federal judges, as affirmed by the Judiciary Act of 1789, aim to protect the independence and integrity of the judiciary. The Supreme Court, since its first assembly in 1790, has maintained a commitment to its foundational traditions while guiding the entire judicial system of the United States.