It very much depends on what state you are in. Here is an example from one state:
First, one party initiates the divorce by filing a petition. The petiion must be served on the other person or they can accept service of the petition. Then that person must file an answer.
Next, any preliminary matters can be settled at a court hearing for emergency custody orders or emergency temporary support or temporary orders regarding the house.
If there are children involved you will often have to undergo a custody evaluation if the parties cannot agree on who will have custody (these can be very expensive). Many time courts will require you to go to a parenting class to learn how to talk to your kids about divorce. Courts may also require the parties to try mediation to resolve any issues in the divorce.
If you are going to be having a trial there may be depositions, the request of records from banks and from both parties. Information will have to be collected and organized by you or your attorney.
You may try mediation or a settlement conference to come to an agreement regarding any issues.
If you have a trial in front of a judge you need to be ready to present witnesses and evidence regarding income levels, support required, custody issues, etc.
The judge will issue a final judgment that will rule your family until it is modified.