This is currently the most common method of divorce. Each side hires an attorney, one of them files the complaint, and the other answers. Then the attorneys begin the discovery process (i.e., finding out about the couple's assets as well as custody and support issues).
The attorney use formal court procedures such as written questions answered under oath (interrogatories), oral questions answered under oath in front of a court reporter (depositions), and subpoenas (use of the court's power to obtain documents from third parties).
The clients agree on what they can, and the attorneys negotiate with each other on the rest in order to reach a settlement. They contact their clients as necessary, and usually send them voluminous copies of all the documents they file and obtain. Sometimes, four-way meetings are held, but the threat of going to court if the process breaks down is always present.
With attorney-negotiated settlements, the Friend of the Court often interviews each spouse and holds hearings in lieu of the judge. The attorneys often hire experts to do such things as business valuations or to perform a custody evaluation. Except for not going to trial it is a traditional adversarial process.