What is a mediator?
Only mediators who have undergone special, recognised training can receive recognition by the Federal Mediation Commission. From then on, they are on a list of accredited mediators. They are seen as people competent to help you if you want to find a way out of your conflict together.
There is a body, the Federal Mediation Commission, which publishes a list of all accredited mediators. You can find mediators in your region and each mediator is listed in what type of conflicts they mediate. For example, if you want to settle your divorce through mediation, you need an accredited mediator in family matters.
For more information, take a look at the website of the Federal Mediation Commission.
A lawyer-mediator offers you just that little bit more....
Many lawyers are also recognised as mediators. If you choose a lawyer who is also a mediator, you already have the advantage that your mediator has the necessary legal baggage to also assist you as a mediator in a high-quality manner.
Or: ask a lawyer to assist you during the mediation talks
You can perfectly well sit around the table with (only) the other party(ies) and a mediator but know that you can always bring a lawyer to those mediation talks as well. That lawyer may not be allowed to speak during the mediation but you can always go to him for legal advice. This way, you will know at any time if you are getting what you are entitled to and you will be in a stronger position during those mediation talks.