Use an Attorney
You're thinking "my case is simple" - but the element of a missing spouse complicates things immediately. Not only will your papers have to be perfect, you'll need to go through some extra steps to accomplish what lawyers call valid service of process, meaning that you've done all one can to give notice of the case to your spouse.
Try to Get an address or town
Google may be your friend. Parents or other relatives may have tips. But when all else fails, your attorney will know that a process server has tools to find people who've left town. The process is known as skip tracing, and the process servers are very good at it.
Ask Your Attorney About Service by Publication
Typically this step requires making a motion in court seeking permission to give notice to your spouse by publishing an advertisement in the local newspaper(s) stating that the case has been started. Each state has its own requirement for proper service by publication, including a rule on whether court permission is required before this method is used - that's one of the reasons you'll need an attorney.
What if the spouse is overseas?
This can be particularly tricky. What steps will be needed to serve notice on your spouse will depend upon the country. However, almost every country has some rule on how to serve notice - many have signed something known as the Hague Convention on service. Your lawyer will know how to handle this part of the problem...but be aware that international service of process can take a considerable amount of time and may delay your case.
Make Sure the Appropriate Affidavit of Service is Filed
If there's no service, there's no jurisdiction. That means the court can't and won't proceed without notice to your spouse. The way the court officially learns of the service is through the affidavit. Your attorney and process server will know the technical requirements for affidavits in your state.