Each party has their own attorney with whom they can discuss - privately - their concerns and goals for the matter.
The clients and the attorneys sign a four way agreement that they will reach an agreement and resolve the case.
The core of that agreement is that the parties agree that they are NOT going to litigate the matter. Now, the parties always have the right to go to court to have a judge resolve their differences, but the four-way agreement requires the attorneys to mutually agree that they will withdraw rather than commencing litigation to resolve the matter. The parties can hire new counsel and proceed traditionally if necessary.
The parties and their attorneys meet and define the scope of the work and the objectives of the parties
This includes agreements regarding payment of attorney fees, spousal support and child support. The attorneys advise the court of the collaborative proceeding. In my jurisdiction, case schedules are suspended so long as the parties are actively working towards a solution.
Experts are hired jointly to advise the parties
If necessary, a financial adviser is hired to review the marital estate and make suggestions regarding the efficiency of different modes of dividing the estate. This avoids the dueling expert problem. Parenting experts can similarly advise the parties of the best means to provide for the children's stability and best interests. A parenting plan that provides for a continuing good relationship between the children and each parent is drafted and agreed.
When each party is satisfied with the agreements reached, orders are entered.
There is no underlying need to litigate a dissolution in the same manner as a contract dispute between two corporations. Rather, the collaborative model can - for the right clients - provide a process wherein two persons can unwind their marriage, deal with their estate, and reach a co-parenting relationship that allows both to have a decent relationship that respects their children's needs.