"Where the Executive and Legislative branches are elected by the people, members of the Judicial Branch are appointed by the President and confirmed by the Senate. Article III of the Constitution, which establishes the Judicial Branch, leaves Congress significant discretion to determine the shape and structure of the federal judiciary." [Source: The White House, The Judicial Branch]
The Supreme Court of the United States - The highest court in the U.S federal judicial hierarchy.
U.S. Court of Appeals - The 94 judicial districts are organized into 12 regional circuits, each of which has a United States court of appeals. A court of appeals hears appeals from the district courts located within its circuit. There is a 13th circuit court, the Court of Appeals for the Federal Circuit, which has nationwide jurisdiction for appeals of specialized cases, e.g. patent law cases.
U.S. District Courts - The trial courts of the federal court system. There are 94 federal judicial districts, including at least one district in each state, the District of Columbia and Puerto Rico.
U.S. Bankruptcy Courts - Each of the 94 judicial districts handles bankruptcy matters, and in almost all districts, bankruptcy cases are filed in the bankruptcy court.
U.S. Court of Federal Claims - Has jurisdiction over most claims for monetary damages against the United States, disputes over federal contracts, unlawful "taking" of private property by the federal government, and a variety of other claims against the United States.
U.S. Court of International Trade - Addresses cases involving international trade and customs issues.