All that it takes is for the parties to agree upon a specific arbitrator and contact that arbitrator to determine if the person is willing to take the case. Where you have agreed to have the arbitration handled according to the rules of a particular association, the association may handle the process for you. For example, the American Arbitration Association has panels of arbitrators. It provides a list of arbitrators and sends it to the parties and they choose an acceptable arbitrator from that list.