How should I prepare to contest this divorce before the petition is filed.
Child Custody Lawyer
Unfortunately you are unable to stop your husband. Anyone may file and obtain a divorce. What contested means is that you challenge the issues that arise during the divorce such as custody or property division and not simply "give into" what he demands.
Divorce / Separation Lawyer
Attorney Szewczyk is correct that in most states you cannot stop a divorce. Unless your spouse will agree to try counseling, it is entirely up to him whether or not he wants to remain married.
The best way to “prepare” is to immediately make an appointment with a local family law attorney. It is preferable to meet with a certified family law attorney or one whose practice consists of at least 75% of family law (Divorce, custody, support and division of property issues)
Make sure you have copies of all the important household papers which include
1) Property: Certificates of title, Deeds and Insurance policies; Stock, Mutual funds and Retirement statements;
2) Financial: Tax returns both state and federal for the last 3 years including W-2 or 1099 statements, recent pay stubs showing the earnings year to date.
It will be also helpful when you discuss 3) Child Custody, to Create and maintain an ongoing log that shows chronologically the time each parent spends with the children and how that time is spent.
You can review attorneys in your local area by contacting your local County Bar Association. Most have a Referral site. Check out the attorneys credential with the State Bar as well as sources such as avvo.com.
Disclaimer: I am licensed to practice law in the state of California. Therefore if your case in not in California, the information contained herein may not apply. This answer is provided as a public service and as a general response to a general question, it is not meant, and should not be relied upon as specific legal advice, nor does it create an attorney-client relationship.