How to prepare for child custody mediation (aka Family Court Services/Concilliation Court) depends on what county you reside in. There are two types of mediation depending on the county which you reside in.
The first type is Confidential Mediation. In this type of mediation, both parties meet with a court-cretified MFT/Counselor that helps the parties develop a parenting plan. The party requesting the mediation appointment has an option of meeting with the other parent or alone. If they meet alone, they will usually meet with the parties twice to hopefully bridge any gap between the parties' positions. If mediation is successful, the mediator will draft an agreement for the parties to take to their court date. There is usually a 10 day grace period for either party to change their mind by faxing a simple letter to the mediator's office. If this happens, then there will not be a mediation agreement when the parties go to court.
The second type of mediation is Reporting Mediation. In this type of mediation, everything that occurs in mediation can be sent on to the court. The similarity with the first type is that if there is an agreement, it is forwarded to the court for the parties' court date. However, regardless of whether the parties agree or disagree, there is a report generated that is sent to the court. As such, it is best if the parties bring a copy of their paperwork or other documentation they have to support their respective claims. It is also essetial to watch your body language and how you conduct yourself with the other party. The mediator has wide discretion in forwarding any information off to the court (yelling, cursing etc.) On the parties court date, the parties will have a copy fo the mediator's report. If they accept the recommendation, the court will make that the order of the court. If the parties disagree, the court will hear rom both parties about their respective concerns with the report and make an order.