Go to the U.S. Department of State website and read the rules for service of process in foreign countries. The rules for different countries are different depending if a country has entered into a treaty to which the United States is a party. Generally, for service to be valid in a U.S. court, it must be valid in the country in which you are serving your spouse. Different countries have different rules. You may be able to serve by mail, by a designated foreign agent or by publication depending on the country.
Fill out your divorce petition to include your name and address, your spouse's name and his address if you know it, when and where you were married, why the court has jurisdiction, your legal grounds for divorce, and a prayer for relief -- a request to the court for specific remedies that is normally written in the concluding paragraph of a petition or motion. Different states require different items in divorce petitions. Read the rules for your state.
File the petition with the clerk of the court and get a file-stamped copy.
Serve the file-stamped copy on your spouse according to the rules for service of process in your state and in the foreign country. The rest of the divorce process is the same as it would be for divorcing a U.S. resident. However, it may take longer. If your spouse does not return to the United States to appear in court, the judge may grant you a default judgment of divorce.