A person who is not a law enforcement official or prosecutor may press criminal charges in two ways: through summoning the police to a crime scene and/or by filing a document called a "criminal information" at the local police station. A state or federal prosecutor may press charges using a grand jury. For a federal crime, you may have to press charges with the FBI.
If you are the victim of a crime or a witness to a crime, dial 911 and tell the operator you need the police. Direct the police to where the alleged crime happened. Tell the police what you know. If you are the victim, tell the police you want to press charges.
If the police do not act or if you have discovered the alleged crime after the fact (which is often the case in financial crime), then go to the police department headquarters and tell the desk sergeant that you want to press charges against someone for a crime. The desk sergeant, the person who tends the front desk of a police station, will fill out a form called a "criminal information" report. The criminal information document is a remnant of English common law that underlays much of state and local law in the U.S.
The police will use the details on the criminal information report form to investigate the matter and make an arrest if appropriate. The prosecutor's office will contact you if it needs you to testify or to provide more information to the court. If you are a victim of a crime, tell the prosecutor that you want to pursue the case and want to testify against the defendant.
If you witness a crime or are the victim of a crime, do not try to catch the person responsible. Call the police as soon as you are safe. Try to take notice of all details of the criminal, including physical characteristics (height, skin colour, hair, weight, tattoos, etc) and type of vehicle or escape route. When in doubt, call 911.
Only file a criminal information report or press charges when you honestly believe that a crime has been committed and person you have identified has committed the crime. Filing a false police report is itself a crime. If you file false charges against someone else, that person may have reason to sue you later. In some jurisdictions, courts may not let certain classes of victims (like domestic violence victims and juveniles) drop charges. The trend in domestic violence cases is to not permit the victims of domestic violence to drop charges once filed, but this occurs only in a minority of jurisdictions. In common law jurisdictions (the vast majority), a spouse cannot be forced to testify against his or her spouse. The police may chose not to pursue the case if there is a lack of evidence to support a conviction.