Article III of the Constitution established the judicial branch of government with the creation of the Supreme Court. This court is the highest court in the country and vested with the judicial powers of the government. There are lower Federal courts but they were not created by the Constitution. Rather, Congress deemed them necessary and established them using power granted from the Constitution. (from Ben's Guide)
Members of the Judicial Branch are appointed by the President and confirmed by the Senate.
Federal courts enjoy the sole power to interpret the law, determine the constitutionality of the law, and apply it to individual cases. The courts, like Congress, can compel the production of evidence and testimony through the use of a subpoena. The inferior courts are constrained by the decisions of the Supreme Court — once the Supreme Court interprets a law, inferior courts must apply the Supreme Court's interpretation to the facts of a particular case.
The founding fathers deemed the courts so necessary, the court's existence and powers are lobbyed for in Federalist Papers 78-83.
A federal civil case involves a legal dispute between two or more parties. To begin a civil lawsuit in federal court, the plaintiff files a complaint with the court and "serves" a copy of the complaint on the defendant.
The judicial process in a criminal case differs from a civil case in several important ways. At the beginning of a federal criminal case, the principal actors are the U.S. attorney (the prosecutor) and the grand jury. The U.S. attorney represents the United States in most court proceedings, including all criminal prosecutions. The grand jury reviews evidence presented by the U.S. attorney and decides whether there is sufficient evidence to require a defendant to stand trial.
Federal courts have exclusive jurisdiction over bankruptcy cases. This means that a bankruptcy case cannot be filed in a state court.
The Appeals Process
The losing party in a decision by a trial court in the federal system normally is entitled to appeal the decision to a federal court of appeals. Similarly, a litigant who is not satisfied with a decision made by a federal administrative agency usually may file a petition for review of the agency decision by a court of appeals.
In a civil case either side may appeal the verdict. In a criminal case, the defendant may appeal a guilty verdict, but the government may not appeal if a defendant is found not guilty. Either side in a criminal case may appeal with respect to the sentence that is imposed after a guilty verdict.
In most bankruptcy courts, an appeal of a ruling by a bankruptcy judge may be taken to the district court.
The Supreme Court of the United States
District (Trial) Courts
There are two special trial courts that have nationwide jurisdiction over certain types of cases; The Court of International Trade and The United States Court of Federal Claims.
Federal Courts and Other Entities Outside the Judicial Branch
information from http://www.uscourts.gov/