It's easy to talk about "the government" generally without acknowledging that, in the United States, we have both state government and federal government. But the distinction may not seem to matter since both types are run by politicians and make laws. Just so, there are enough similarities between the federal court system and the state court system to make it easy to lump them together. For starters, both are required to apply and enforce the laws.
Federal and State Courts
The federal/state court divide is actually linked to the federal/state government divide. That's because federal courts are created by federal law that applies to all of the states and territories of the nation. On the other hand, state courts are created by laws enacted by each state government.
While the structure of federal courts and state courts differ, the actual courtrooms look a lot the same. Both state and federal courts have judges (also called magistrates or justices) that sit at a tall bench in the front of the courtroom and play important roles in cases brought before them. First, they keep order in the courtroom and decide whose turn it is to speak and for how long; most importantly, they listen to and review the evidence presented and apply the law to the facts to make a decision. Both state and federal judges have the power to sanction attorneys or parties who fail to obey their instructions.
The roles of judges are largely the same regardless of which court they sit on. Both federal and state judges hear arguments about preliminary issues in cases, brought to the attention of the court via filings called motions or petitions. Judges consider the different propositions and make rulings. And in cases with jury trials, judges in both state and federal courts are responsible for making rulings on issues of law.
Court Rules and Procedures
Both state and federal courts expect parties and attorneys to behave well when they are appearing before a judge. Both systems enact written Rules of Court that provide mandatory procedures as to how a case is conducted. Since state and federal courts handle criminal as well as civil cases, both have rules of civil procedure and rules of criminal procedure that apply and are enforced. The federal rules are quite different from the state rules, and state rules also vary from state to state. That's why many attorneys specialize in either state or federal actions.
One set of procedures used in both state and federal court is the mandated exchange of information between the parties. This is called discovery. While TV programs sometimes show an attorney shocking or amazing the other side by bringing in the smoking gun at the last moment, this doesn't happen so much in real trials. Under the rules of discovery in both systems, a party has to provide the other side with all pertinent evidence before trial. This is particularly true in criminal cases where the prosecutor cannot withhold exculpatory evidence from a defendant without violating the Constitution.
Appeals in Federal and State Courts
The justice system in this country is a many-layered one. Whether you go to federal or state court with a case, you are not necessarily stuck with the first result. If it seems unfair or just wrong, you can appeal a federal district court ruling to the Circuit Court of Appeals. If you are still unhappy with the decision, you can ask the U.S. Supreme Court to review the case. This latter appeal is discretionary in most cases, and the Court decides whether it hears your appeal.
In state court, you also get a chance to have your decision reviewed. While state court designations differ between states, all states have "trial" courts and appeal courts. For example, in California, you go to trial in the superior court in the appropriate county. If you lose and want to take it further, you can appeal to the appellate court. The final appeal in state courts is identical to federal courts: you can ask the U.S. Supreme Court to review your case if constitutional issues are involved. The Court can opt to review or not to review in most cases.