What is the process for starting a divorce if you don’t know where your spouse is?

To file for divorce, you must notify your spouse of your intentions; they need to be afforded the right to be heard in court. To start, you will need to file a "Summons and Complaint", and have your spouse personally served. If your spouse cannot be found then in that case, you can "serve" a divorce complaint via "notice by publication". This is used when a spouse cannot be located.

Basically, the absent spouse is notified of the divorce proceedings by publishing notice. Specifically, you will have to present proof to the court that you made a genuine effort to locate your spouse. You will have to show convince the judge that you checked with family/friends, voting records, the phone book, DMV, etc. Basically, that you utilized any and every source that would likely lead to uncovering the missing spouse's current location.  Once you have demonstrated to the the court's satisfaction that you have made a thorough search, you will be allowed to serve your spouse by publishing notice in a newspaper (as opposed to the more usual method of personal service).  The court will instruct as to which paper should be used (typically one in the area of your spouse's last known address).  

Once your spouse is in "receipt" of the summons with complaint (via the newspaper notice), they have about 20 days to respond. If they fail to do so within the 20 day period, then they will be considered in default. You may then petition the court for a "Default Judgment". If the courts grant your request for a default judgment, it will be granted according to the stipulations listed in your Summons and Complaint.

This is just a brief overview; you really should consult with a local divorce attorney as to the details of this whole process.