File an Answer or Response to the Petition for Divorce, which should have been served on you or your representative by an authorized process server. You will have a statutory deadline for filing; a common period of time in many civil courts is 20 days. The Answer should state your grounds for contesting the divorce petition. If you are unable to file the Answer within the deadline, request an extension of time from the court with good cause for the late filing.
Prepare for a hearing, at which you will state your case for contesting the divorce. You may contest any grounds for divorce asserted by your spouse with documents, other evidence and/or witness testimony. Your spouse has the right to rebut this evidence; the court will decide if the asserted grounds for divorce are valid. All states provide for "no-fault" divorce, in which "irreconcilable differences" or some other generalized condition is given as the reason for the divorce. You cannot have such grounds overturned in court; if this is the case, you can only contest the proposed terms.
Explain to the presiding judge any challenge you are making to the terms of the divorce set forth in a proposed marital settlement agreement. In the matter of child custody, for example, you may need to prove that you are more fit to serve as the child's custodial parent. For child support or alimony payments, you may have to present evidence that you are unable to provide the monthly amounts requested. You may also contest a proposed division of property, such as title to a home or property held in common with your spouse.
Listen to the judge's decision on contested grounds or divorce terms. The judge must provide grounds or precedent for his decision, which must be guided by state law and its intent. You may appeal this decision, or in some states file your own proposed marital settlement agreement, which can then be negotiated between the parties. The court may also refer the case to mediation.