This post is a very broad look at mediation as it is practiced in Texas, specifically in Tarrant County, Texas. Please don't assume that my comments accurately describe mediation as it is practiced in other states.
1. Who is the mediator? The attorneys in the case will normally choose the mediator, although the judge in the case might make the decision. They consider mediators they have had success with, ones with personalities compatible with the parties or ones with special knowledge or experience with the issues that will come up. Most often, the mediators are local attorneys. Sometimes they are retired judges. In some cases, two mediators are used. Mediators are specially trained in mediation and family law. They normally have strong communication skills and are very good listeners.
2. What is the format? In Texas, most cases use the caucus system which means that each side is in a separate room and the two sides don't usually come into contact with each other during the mediation. Each side has their own attorney who actively participates in the process. In other states, the mediation takes place in joint sessions and attorneys don't participate in some areas. Mediators can work under either system. In the beginning, the mediator introduces himself or herself to the parties and gets some general information. The mediator asks one or both sides for opening offers which are then conveyed to the other side. The mediator goes back and forth, meeting with the parties, asking questions and keeping the discussion moving. Part of the mediator's job is to get the parties to consider other points of view. That's helpful in breaking through impasses. After many trips back and forth, the mediator can usually help the parties reach agreements.
3. How do you know what to ask for? It's a good idea to spend time prior to the start of mediation in figuring out what you want to end up with. Once you are clear on what you want, then you can come up with some opening and secondary positions to use to start the process and keep it moving. Equally important is to think about the motivations and interests of the other side. If you can figure out what they are likely to be aiming for, you can plan your moves to maybe achieve both your and their objectives. Maybe you can come up with some trade-offs. Planning ahead will make it easier to come up with ideas that can work.
4. What should be your strategy? Keep your goals in mind. Leave yourself room to compromise. You should never start off requesting your best result. No matter how logical or reasonable you think it is, the other side is not going to accept your opening offer. Some people take an almost opposite approach, which is also usually a bad idea: start off with the toughest issues to test the other side and find out if they are willing to compromise. It's usually better to start with some easier issues and create momentum in coming to small agreements. That can lead to bigger agreements. Special warning: Don't expect logic or rationality to plan much of a role in settling a family law case.
Be sure to talk with your attorney and prepare ahead of time. The attorney can answer any questions you have about how mediation works. You should go in expecting to be successful!