After arraignment, the case proceeds to hearings before a judge that is assigned to the case from that point on. Most, but not all, judges schedule what is called a pretrial.
The pretrial is an opportunity for the prosecutor and defense attorney to discuss the charges, motions to suppress evidence, motions in limine, and the relative strengths and weaknesses of the case. In some cases, the matter is scheduled for additional pretrials to speak with witnesses or review other evidence or legal issues.
In many cases, the pretrial will be the first time that the prosecutor makes a plea bargain offer. A plea bargain is essentially what the prosecutor is willing to accept short of taking the case to trial. If the defendant accepts the plea bargain, the plea is taken before the judge in open court and the defendant is adjudged guilty of whatever criminal offense is agreed upon.
In misdemeanor cases, the judge will generally proceed directly to sentencing. In felony cases, the matter is generally referred to probation for a pre-sentence investigation and scheduled for a sentencing hearing.
If the plea offer is rejected, the case proceeds to trial, either to the judge or to a jury.