Check sources such as a map of the North American Insulation Manufacturers Association to determine the amount of insulation needed. It recommends a heat resistance, or "R value," of 2 1/2 to 5 for most of the United States, a level that 1 1/2 inch XPS will provide. Buy foam board with grooves if possible to drain away any soil moisture that accumulates outside of the wall.
Cover the wall with good waterproofing, such as some type of asphalt. Let the moisture barrier dry thoroughly before setting any rigid foam board against it. Get foam panels tall enough to extend from the ledge on the concrete wall footing to the projected finish height of the soil around the wall. Panels can be obtained in lengths of 9 feet or more.
Set the first panel in place at one end of the wall, with the bottom on the foundation footing and exterior grooves vertical. Run a bead of sealant, compatible with the foam board and recommended by its manufacturer, across the top of the panel and press it firmly in place against the wall. Secure the panel with two concrete fasteners with 1-inch corrosion-resistant washers on the caps. Put fasteners a few inches from the edge of the panel. Use fasteners long enough to penetrate the foam board and 1 1/2 inches into the concrete.
Apply foam board with a construction adhesive as an alternative, depending on the manufacturer's recommendation. Dow, creator of Styrofoam and a leading producer of foam board, recommends mechanical fasteners. Install an exterior protective layer over any foam board on the foundation, which will extend above ground level. Run this several inches down the exterior to seal the area.
Add other panels across the wall. Butt the panels tightly together if they do not have tongue and groove connections. Cover the bottom of the panel, the concrete footing and any perimeter drainage system with several inches of some coarse granular material once the wall is insulated. Grooves in the panels will drain surface water down to this area to prevent it from collecting against the wall.