Insert a tube of construction adhesive into a caulking gun. Cut the tip off and insert a nail into the nozzle to release the adhesive. Use a construction adhesive designed for both foam and drywall surfaces. The wrong adhesive can eat through the foam.
Apply continuous lines of the adhesive around the edges of the drywall board. Keep the adhesive at least two inches from the edge because it expands as it dries.
Press the drywall against the Styrofoam and smooth it into position so it lays flat. Work quickly because the adhesive is permanent once it sets.