In order to have a case in court, a prosecutor must file charges against you. Typically, the police refer the case to prosecutors, who then review the reports and decide whether or not to charge you, and what to charge you with. You will then either be notified by mail (this is called a court summons) or a warrant will be issued for your arrest.
Your first appearance is typically an Arraignment. This is a simple hearing where you are informed of the charges filed against you, and given a written copy of the document charging you. In courts of limited jurisdiction (District and Municipal Courts), the charging document is called a "Complaint" and it specifies a misdemeanor violation. In Superior Court, the charging document is called an "Information" and it charges you with a felony. Your lawyer will typically waive formal reading of the document so that the court doesn't have to read it out loud in front of the entire courtroom.
At the Arraignment, you are asked if you are the person named in the charging document. Typically you will answer "Yes" and that is the ONLY thing that you will be expected to say at the hearing. In virtually every case your lawyer will then enter an initial plea of "Not Guilty", even if it is your ultimate intention to plead Guilty. This Not Guilty plea is the starting point for all of the court processes that follow. Note that in Superior Court your personal appearance is required at the Arraignment. For misdemeanors in District or Municipal Court, an attorney can waive your appearance and appear for you, except in DUI or Domestic Violence cases, where your personal appearance is required.
Another item of business typically taken up at Arraignment is the conditions of your release pending trial. Typically the prosecutor will recommend to the court that you be released on some amount of bail, or your own personal recognizance (PR), without having to post bail. Your attorney has an opportunity to argue for reducing the bail or asking for a PR release, but he has only one chance to make the bail motion, so he should be prepared at Arraignment to do so. Sometimes it will be more advantageous to postpone the bail hearing until your lawyer has more information, and in that case your lawyer should "reserve bail". The court will then leave whatever previous release conditions were in place until a scheduled bail hearing.
Finally, the court at Arraignment will set the date of the next court appearance. The next appearance is usually some kind of "pretrial conference" or "case setting conference", depending on the jurisdiction, but it's almost always the first opportunity for your lawyer to discuss with the prosecutor what's going to happen with the case (i.e., will there be a settlement or will it go to trial). Sometimes nothing happens at a pretrial hearing other than the lawyers confirming that they still have more documents and evidence to exchange, and then continuing the case to another pretrial hearing date. This is quite common in criminal cases and you should expect a number of these pretrial court appearances before you are scheduled to have an actual "trial". Don't assume that nothing is happening when your lawyer continues your case to another court date. There's a lot going on behind the scenes, and most of these pretrial court hearings are just "checkpoints" provided by the court to give the lawyers an opportunity to confirm the progress of the case. It usually takes several pretrial hearings before the case is ready to be resolved through plea negotiations or trial.
In Superior Court, there will be one final court appearance before the trial, called an "Omnibus Hearing". This is the final checkpoint before trial and is an opportunity for the prosecutor and defense lawyer to confirm readiness for trial.