Fill out divorce papers and a divorce petition. This can be done at your county courthouse. If your spouse is out of the country, you may want to consider hiring an international lawyer to help with the process. Your initial paperwork will need to include a suggested divorce settlement, lists of any marital assets and any child custody information. If your spouse has any marital assets he has taken with him out of the country, your chances of recovering the assets varies by country. A good international attorney can advise you.
Serve the paperwork on the person out of the country. An international divorce attorney can help with this step. Depending on your state's divorce laws, you may be able to "serve" the spouse via publication in the other country. Or your state may require that you attempt personal service by mail or by an international process-server before publication.
Proceed with the divorce. Once service has been completed, the other person out of country still has the option of fighting or responding to the divorce proceeding. She may appear for a hearing in front of the judge in your state or could even be allowed to have a teleconference with the judge. If the person out of the country does not respond to any divorce-proceedings service, each state has a specific waiting period before proceedings can continue without the other party.