Sweep the concrete surface to remove any dust or dirt. If necessary, wash it with warm soapy water and rinse well. Remove any grease spots with degreasing cleaner. Let it dry completely. Patch any holes in the concrete and let the patched areas dry.
Cut the foam insulation panel to fit the concrete area. Vacuum or blow away all the foam debris from the concrete so it will not get stuck in the adhesive.
Squeeze a bead of industrial adhesive designed for use on foam insulation on the concrete. Outline the concrete area with a continuous line of glue about 3 inches from where the edge of the foam panel will be. Apply a bead down the middle of the area as well. Do not use a petroleum-based adhesive because it will dissolve the foam insulation. Some adhesives recommend different directions, so follow the label directions on the adhesive packaging closely.
Press the foam insulation panel to the concrete within a few minutes. Place it carefully because some adhesives do not allow you to move the foam once it contacts the glue. On the other hand, some adhesives instruct you to press the board into the glue then pull it away for a couple of minutes before pressing it back onto the concrete. Read and follow label directions for your particular adhesive.
Wedge boards against the floor and against the foam insulation to hold it in place for 24 hours while the glue dries.