Wrap the exterior sheathing -- typically plywood or oriented strand board -- with a moisture or vapor barrier before you install EPS foamboard. Staple the vapor barrier to the sheathing with a construction stapler. Snap a level chalk line the length of the wall 3/4-inch above the bottom of the sheathing as a starting point for the EPS panels.
Place the first panel at one corner of the wall. Align it on the bottom with the chalk line, and use a straight board at the wall corner to align it vertically. Nail panels to the sheathing and underlying wall studs with wide-head aluminum or galvanized-steel nails and a hammer. Drive nails into the studs every 16 inches horizontally and at least every 2 feet vertically. Don't pound the nail deeply into the foam.
Butt the panel edges tightly together. Better yet, buy foamboard with tongue and groove connections, so that one panel edge slides into the other. Cover the entire wall, including doors, windows and other openings. Overlap the panel edges at wall corners. Use a utility knife, drywall saw or reciprocal saw to cut out openings after the wall is covered. You may have to cut small holes for water or electrical outlets first to get the panels properly on the wall.
Tape all seams with special tape, usually provided with the ESP. If it's not provided, use tape from the same manufacturer that produced the ESP. Tape around door, window and other openings so that there are no gaps or openings to allow moisture to penetrate the ESP. Tape all wall corners..
Use a similar technique to install ESP on roof decking, but use foamboard dense enough to support the weight of workers on the roof. Do not crush or dent ESP foamboard. Buy foamboard with a vapor barrier on one side for roofing. Put the barrier face-down.
Install ESP for interior insulation by placing it between studs in the walls. Use panels to match wall cavities, typically 16 inches wide and 3 1/2 inches deep. Cut panels with a utility knife or drywall saw as needed to fit between studs and around wall bracing, electrical outlets and other openings. Seal the seams with tape, and cover the interior with a vapor barrier if the panels do not come with a vapor facing. Put the vapor barrier on the inside of an interior wall.