Lay newspaper over your work surface to protect it from the spray adhesive you'll be using.
Cut the Styrofoam with sharp scissors or a knife, if necessary, for your craft project. Since it comes in many sizes of balls, sheets, cones and domes, you may already have exactly the shape and size you need.
Apply the spray adhesive to the Styrofoam according to the directions on the adhesive's label. Hold up the sheet of moss and spray the back of that, as well.
Lay the sheet of green moss over the Styrofoam and press it gently into place. Let it dry completely before continuing the project.