How does the divorce process work if the person you are married to has been gone for 4 years with no contact and you don’t know where they live now?

In any lawsuit the non-filing party must be notified of the action. This is to ensure that they have a chance to be afforded the right to be heard in court.
A divorce action is a lawsuit, so the party seeking it (the "Petitioner") needs to file a valid "summons and complaint", and have their spouse (the "Respondent") properly served. When a spouse can't be located, then they can be "served" what is known as "notice by publication". Basically, the missing spouse is notified of the divorce by publishing notice of the proceedings. Specifically, the filing spouse will have to present proof to   judge that they made diligent efforts to find their missing spouse; they must convince the court that they utilized every source that could lead to discovering the absent spouse's whereabouts. Once done, the court will be allow the petitioner to serve the respondent 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 (generally one in the area of the respondent's last known address).  
Once the respondent is in "receipt" of the summons and complaint, they have about 30-60 days to respond (it varies from state-to-state). If they fail to do so within the specified time, then they will be considered to be in "default". Then, the petitioner, may then request a "default judgment" from the court. If granted, it will be on the terms that the petitioner requested.
This is just a brief overview. You really should consult directly with a local divorce attorney for further advice.