How canyou get a divorce if you don’t know where your spouselives?

In a situation such as this there is a legal remedy known as "divorce by publication". In a legal proceeding the concept of "notice" is crucial. Legal action should not be taken against someone without giving them opportunity to appear and explain their side of things (in this case, to answer the complaint of divorce). Consequently, even if a spouse can't be located they still must be notified of the divorce action before it can proceed. This is what a "divorce by publication" accomplishes.

Briefly this is the way it typically works. You as the filing spouse (i.e. Petitioner) must make a good faith effort to find your missing spouse (i.e. Respondent).  You will have to present proof to a court that you made every effort to locate them. To prove this you will have to show the court that you checked with family/friends, voting records, the phone book, DMV, and any other source that would likely lead to uncovering their current whereabouts.  Once you have demonstrated to the the court's satisfaction that you have made a diligent search, you will be allowed to serve your spouse by publishing notice of your divorce in a newspaper (as opposed to the more usual method of personal service).  The court will instruct you as to which paper should be used (typically one in the area of your spouse's last known address).  

Generally, in most states, the Respondent has 30-60 days to file a reply after the first day of publication. If they fail to respond within that time, the Petitioner then files a request to enter a default dissolution of marriage. It is generally granted upon the terms requested by the Petitioner (although the Respondent is given a certain time limit in which they can appeal).