By complaint, information or indictment.
THESE COMMENTS ARE NOT LEGAL ADVICE. They are provided for informational purposes only. Actual legal advice can only be provided after consultation by an attorney licensed in your jurisdiction. Answering this question does not create an attorney-client relationship or otherwise require further consultation.
In state court in Arizona, a felony may be initiated by a complaint and information or by a grand jury indictment. A misdemeanor is usually charged by way of complaint, although a grand jury can add a misdemeanor charge in an indictment which also charges felonies.
A complaint states the allegations under oath and is filed with the court. It is sent out by a summons or a warrant may issue. When there is a complaint, the defendant is entitled to a preliminary hearing, and will have an attorney present to cross examine the state's witness or witnesses. This is a "probable cause hearing" meaning is there probable cause to believe a crime was committed and probable cause to believe the accused committed it.
A grand jury indictment occurs when a group of 9 or more people on the grand jury decide that an indictment should issue because there is probable cause to believe a crime (or crimes) have been committed and the accused committed them. This is done behind closed doors and the neither the accused nor his attorney is present. In Arizona, however, after arraignment, the accused is entitled to obtain the transcript of what was presented to the grand jury and, if appropriate, challenge the indictment as faulty in certain ways. This is done under rule 12.9 of the Arizona Rules of Criminal Procedure.
Federal courts may initiate felonies and misdemeanors in the same ways. However, in federal court it is a difficult process to obtain a copy of what was presented to the grand jury, and it may never occur.
I'm not sure if that answers all of the question, but it's a start.
A criminal charge can be brought by complaint, information or indictment. A complaint is generated by the police. An information is generated by the State's Attorney's Office. An indictment is a result of bringing information before a grand jury and asking it to bring certain charges against the individual at issue. Whether a charge is a misdemeanor or felony depends on the qualifying elements involved.