Apply construction adhesive to the face of a 2-by-8 foot sheet of 2-inch-thick rigid foam insulation. Place the adhesive in small blobs in a grid pattern with each blob separated by about 12 inches.
Press the rigid foam sheet against the exterior face of the wall, with the sheet in an upright position. If you are using rigid foam sheets with stepped or tongue-and-groove edges, be sure that they are joined tightly together.
Cut the sheet off so that its top is even with the top of the basement wall. If the basement wall is higher than an 8-foot foam sheet, add another section of foam sheet to reach the top of the wall.
Cut a foam sheet lengthwise to fit the remaining wall space when you reach the end of a wall. When you begin the next wall, position the sheet at the edge of the foam on the first wall rather than the edge of the concrete so you have a continuous covering of 2 inches of foam around the corner of the wall.
Cut around window and door openings with a sharp utility knife after the foam has been attached to the wall. This is easier and more efficient than measuring and cutting before applying the rigid foam. Go inside the basement and trace around the inside of these openings with the knife to cut them out.
Tape the joints between the rigid foam sheets with construction tape. Taped-together rigid foam sheets act as a vapor barrier, so no plastic vapor barrier is needed.
Backfill around the basement walls, being careful not to disturb the rigid foam sheets or place any large or sharp rocks against them. Rigid foam is impervious to water and moisture, so the soil can be backfilled against it without damaging it.