Generally a mediator is appointed to meet with both parties in order to help them to come to an agreement or negotiate a settlement on the matters. He or she can help them to identify the issues they need to overcome and/or suggest solutions to overcome them. Its also of benefit where there is a risk of emotions running high and getting in the way of resolving the situation.
If its using a free mediation service at a court or similar, then usually you would have to apply then you would be allocated a date and time to show up at the court. You would not have a choice of mediator. Alternatively, you can arrange a private mediation - you would need to agree on a mediator and pay them (usually they are a barrister or similar) and each party could bring their own solicitor.