If it is unrealistic to settle the case, your case proceeds to trial. Some cases in which the parties' respective demands are so divergent simply have to proceed to trial in order to resolve the case (e.g. the Wife wants to remove the children to a distant state but the Husband, whom regularly provides support and exercises visitation, will not agree).
Shortly before trial, the judge often wants to conduct a pre-trial conference, which is a more informal way to try one last time to settle the case, but this time with the direct assistance of the judge. In the judge's chambers the lawyers explain the facts of their respective cases, and the judge may give some settlement recommendations. Either party may accept or reject the recommendations of the judge.
If the case does not settle at the pre-trial stage, it is off to trial. Because there are a multitude of divorce cases, and often not enough divorce judges available, parties often wait over a year for trial from the time the divorce process first starts.
Just as you have seen on television, a divorce trial starts with opening statements and ends with closing statements. In the middle, the Plaintiff (often called the "Petitioner" in a divorce case) calls his or her witnesses and attempts to have certain exhibits introduced into evidence. Often there are objections and other motions to be dealt with throughout the Petitioner's case-in-chief. After the Petitioner rests his or her case, the other spouse (called the Defendant or "Respondent" in a divorce case), commences his or her case-in-chief, then rests. Sometimes the Petitioner is allowed limited time to rebut new factual allegations raised in the Respondent's case.
After closing arguments, the judge usually takes a few days to review notes, exhibits, the law, and to make a decision. After the judge makes the decision, one of the attorneys then types up the oral ruling, then the written judgment is signed and entered by the judge, at which point the parties become divorced. If a party does not agree with the judge's ruling, that party has to ask the judge to reconsider its ruling in a written motion or file a notice of appeal within 30 days of entry of the written judgment.
There are no jury trials, only bench trials, in divorce cases in Illinois.