The court system can be seen as a snarled, confused tangle of too many rules and procedures. Some people revel in "their day in court" and can't wait to stand up before judge and jury and have their say; others dread the often tense procedures that can be fraught with emotional pitfalls and angry confrontation. Whatever your viewpoint, the court system is one of the foundations of the U.S. legal system, and has had an enormous impact on how we live our lives.
Both civil and criminal courts are based on the "adversarial model." The theory behind this is that if two parties argue their version of the facts and their interpretation of the law, the truth will emerge. This is why each piece of evidence has to be scrutinized by both sides and each witness must be questioned by each party. For each piece of evidence, one side will attempt to show that it is credible and supports their position completely, and the other side will try to shatter its credibility or show that it doesn't matter to the case. This is the model for both civil cases -- in which two private parties argue -- and criminal cases -- in which the government seeks to prove that someone has committed a crime.
Court procedures vary by state, by region, or sometimes even by court. Regardless of the court you're sitting in, the procedure is in place to ensure that each side gets a chance to tell his story, as well as the chance to examine and challenge his opponent's story.
Because legal procedures can be difficult to follow, people who enter court have the option of hiring an attorney. Attorneys are experts in argument and procedure, and can navigate trial for you. They can also craft the best arguments possible as long as you provide your attorney with all the necessary information. Since the stakes in criminal cases can be so much higher than those in civil cases, the criminal defendant's right to an attorney is protected by the Constitution, and if a criminal defendant facing jail time cannot afford an attorney, the government will provide one free of charge.
See FindLaw's sections on Litigation and Criminal Procedure for more information about courts.