When a problem must be settled before trial and the parties cannot agree, one of the parties may request a motion hearing before the court. Motions may be used to ask the court to make the other party turn over evidence or to enforce the decisions made by the court in earlier orders. Sometimes the temporary relief order must be changed when there has been a change in the facts or an important problem was overlooked at the first hearing.
The Minnesota Judicial Branch maintains a helpful section on divorce at its website, including matters of children and property, an overview of the fees involved in the process, paperwork, and what to expect when you go to court. The site also has a guided flowchart to help you determine which forms you'll need. Also, see FindLaw's article on same-sex divorce.
The summons is a simple legal notice that a divorce action has been commenced by the petitioner and advising how long the respondent has to serve an "answer" to the petition. It also contains a preliminary restraining order, preventing changes in insurance coverage and the disposition of property, except for the necessities of life or in the ordinary course of business. In Minnesota, unless the petitioner agrees to an extension the answer must be served within thirty days. If you ignore the service of a summons and petition for a longer period of time, the petitioner may serve a motion with the court requesting that default judgment be entered. This judgment will not only immediately dissolve the marriage terminating certain rights you have as a married person to rights such as health insurance. It may also result in the moving party being awarded rights and interests in property, as well as the loss by the respondent to certain rights, such as spousal maintenance (alimony) without the respondent having the opportunity to respond and defend their rights. While there are cases in which the court will subsequently set aside a default judgment, it is very important that you retain a lawyer to respond to a summons and petition within thirty days. Sometimes that response may be as simply as an agreement from the petitioner's attorney to extend the thirty day period to answer the petition.
If you are represented by an attorney, the question will arise whether your attorney should attend the divorce mediation with you. This is something you'll work out with the mediator, your attorney, your spouse, and your spouse's attorney. Very often, family law mediation sessions involve just the divorcing spouses and the mediator. This keeps costs down and ensures that you and your spouse do the talking and make the decisions (lawyers have a tendency to take over when they are present).
Court rules now require both sides to try ways other than court to resolve their differences. There are many other ways to reach agreements called alternative dispute resolution (ADR) methods. Make sure you know all your choices before deciding on a method. The parties may be asked to pay for the cost of ADR. Most ADR methods let you stop the process at any time without reaching an agreement.
In reality, every divorce requires both formal legal procedures as well as some kind of settlement negotiations. In Minnesota, even if you prefer to litigate and leave every decision up to the judge, the rules require that before the Court will decide your case, parties must attempt resolution through some form of Alternative Dispute Resolution, of which mediation is still the most common. 
Early Neutral Evaluation (ENE) in Family Court Cases - For parents who are getting divorced, this statewide program connects them with judges and evaluators early in the court process to give them an opportunity to settle their legal issues. Parties can choose to participate in one or both types of ENE: a Financial ENE (FENE) to settle financial disputes; and Social ENE (SENE) to settle custody and parenting time issues involving their children.