The United States, being a federation, does not have a single court system. Instead, it has fifty wildly varying state court systems, and a federal court system that covers the entire country. American law students learn the basics of the federal court system in their Civil Procedure course during the 1L year, and if they're really masochistic, can then learn the gritty details in a separate course called Federal Courts. So needless to say, a single E2 writeup can't describe the whole shebang: this writeup will try to provide an overview.
Federal vs. state courts
Federal courts are said to have "limited jurisdiction." What does this mean? State courts can hear any case based on any legal theory. Federal courts, on the other hand, demand to be told why they should hear the case.
There are several ways to get a case into federal court. There's federal question jurisdiction when the plaintiff raises a question of federal law in their complaint, and supplementary jurisdiction when both federal and state law issues are raised. There's diversity jurisdiction when the plaintiff and defendant are from different states and the suit is for a lot of money, regardless of whether federal law is involved. Federal courts can also have jurisdiction when the federal government is a party to the case.
Note that these are situations in which a case can be brought in federal court. A purely federal issue can be (and often is) litigated entirely in state court. When federal jurisdiction is available, a plaintiff simply has the choice of filing in either federal or state court. However, any party to the case can apply to have the case transferred from state court to federal court, and vice versa; state judges can also send questions of federal law to federal courts. So there's plenty of room for lateral movement across court systems.
History of the system (if history bores you, skip to the next section)
The first court established under federal law was the Supreme Court of the United States, which was created by Article III of the Constitution. Article III specified no other federal courts, and gave few details about how to run the Supreme Court: instead, it delegated that power to Congress.
Congress exercised that power by passing the Judiciary Act of 1789. The 1789 Act set the size of the Supreme Court at six justices, and created two types of inferior courts: District Courts to handle admiralty cases and small claims, and Circuit Courts for appeals, interstate lawsuits, federal criminal cases, and suits in which the federal government was the plaintiff. The district courts (one in each state) each had a local judge, while the circuit courts (also one in each state) consisted of the local district court judge plus two Supreme Court justices "riding circuit."
The District Court system has since remained intact with only minor changes, but the second tier of courts has been in constant flux. In the Judiciary Act of 1801, an outgoing Federalist Party majority in Congress abolished the institution of riding circuit, which was wearing the Supreme Court justices out very quickly: instead, Congress appointed three new "circuit judges" to each of six new judicial circuits. Each circuit corresponded to several district courts.
This system, remarkably similar to what we have today, had a very brief lifespan. The Judiciary Act of 1802, passed by Jeffersonians in Congress, redefined the circuit courts so they would consist of one district judge and one Supreme Court justice. The judge was able to hold trials without the justice: the justice was only needed to hear appeals from the local district courts. The number of circuits grew to eight in 1807, ten in 1837, and eleven in 1855, falling back to ten in 1863 when the District of Columbia lost its separate circuit court.
As the number of circuit courts grew, the number of Supreme Court justices also grew, peaking at ten in the 1860s. The number was cut back to seven in 1866 and finally settled at nine in 1869, where it has stayed ever since, despite some valiant attempts by Franklin Roosevelt during the New Deal era.
The Judiciary Act of 1891 created nine new United States Courts of Appeals in the existing judicial circuits, and these took over the appellate functions of the circuit courts. The circuit courts remained intact for trials until the Judicial Code of 1911 transferred their trial jurisdiction to the district courts.
More circuits were created to keep up with the growing demand for courtrooms: the D.C. Circuit in 1893, the 10th Circuit in 1929, the 11th Circuit in 1980, and the Federal Circuit in 1982. There are also plans to create a 12th Circuit, although those have yet to be passed by Congress. As demand grew, the number of judges also grew: each circuit eventually had a number of dedicated circuit judges, appointed for life like their Supreme Court counterparts.
Levels of federal courts
There are now three basic levels in the federal court system:
There are a few other federal courts, too:
There is some distinction between "Article I court
s" and "Article III court
s." An Article III court, like the courts in the three basic levels, has judges appointed for life at fixed salaries. Article I courts, such as the Tax Court, have judges appointed for fixed terms, and variable judge salaries which are periodically changed by Congress. Article III courts are the truly independent portion of the American judiciary: although they are created by acts of Congress, they are free to shoot Congressional legislation down whenever they see fit. Article I courts, on the other hand, can theoretically be closed up or shut up as Congress wills.