How does someone file for a divorce from someone who is homeless?

  I assume what you mean is how do you serve someone who is homeless.  The Georgia Civil Practice Act allows for "service by publication" in certain circumstances.   In general, when the person on whom service is to be made resides outside the state, or has departed from the state, or cannot, after due diligence, be found within the state, or conceals himself to avoid the service of the summons, the court may grant an order that the service be made by the publication of summons.  To do that, you will have to comply with certain statutory requirements, like filing an affidavit or a verified complaint stating that a claim exists against the defendant in respect to whom the service is to be made, and that they are a necessary or proper party to the action.  Your attorney can assist you with this.