Since moving to Hawaii, I have encountered the most non-law affiliated people I've known since college. When people find out I'm a lawyer, they inevitably ask what kind of law I practice. Fair question. When I respond, "appellate law" or "I'm a clerk" or "I work for the Judiciary" I get a courtesy "oh cool" but a clearly blank expression explains it all. It seems like unless you are a prosecutor or defense attorney or "corporate lawyer" no one has any idea what the hell a lawyer does. Last week I had a conversation with someone who didn't really understand how the U.S. court system worked. It occurred to me that maybe, as law students and lawyers, we take for granted that people
So here is my effort at explaining it. The U.S. judicial system is composed of a federal system and state system. The federal court system is divided into numerous geographic units and various levels of hierarchy. Similarly, each state has its own court system with various local "trial" courts and heirarchical "appellate" courts. Under this dual federal/state court structure, the federal courts decide federal law or issues that arise under the federal constitution. The highest court of each state, (usually) the State Supreme Court, has the ultimate authority to interpret State law. For example, if you get arrested for a crime (generally) or you want to sue someone who lives in the same state as you for money (generally), you'd be in state court. If you get arrested for being part of a multi-state gang conspiracy or you sue someone who lives in a different state from you for more than $75,000, you'll (generally) be in federal court.
The federal judiciary and the individual state judicial systems are each constructed like a pyramid. Entry-level courts at both the state and federal levels are trial courts, in which witnesses are called, other evidence is presented and the fact-finder (a jury or sometimes a judge) is called upon to decide issues of fact based on the law (i.e. were you really drunk? was the light really red? did you have a contract?). At the top of each pyramid structure is the court of last resort (at the federal level, the U.S. Supreme Court; at the state level, the state supreme court) which has the authority to interpret the law of that jurisdiction. In most states and in the federal system there is also a mid-level court of appeals. When you lose in the lower courts, you can "appeal" to the higher court and ask the higher court to say that the lower court got it wrong. Any court has the power to declare a law or government action to be unconstitutional, subject to review by a higher-level court.
Below is a graph of the FEDERAL SYSTEM:
Here is a a graph of the HAWAI'I SYSTEM (NOTE: this is a couple years old. The Intermediate Court of Appeals has 6 judges, the Supreme Court currently has 4 sitting justices and one vacant spot waiting to be filled):
Update: Here is a less detailed chart that makes the court hierarchy a little more clear (click to enlarge):
There is so much more I could try to explain, but hopefully this gives some idea.