Remove any baseboard molding around the room.
Set a laser level to the desired height of the wainscoting (this project was 53-1/2 inches) so everything will be nice and level. Measure from the laser line down to where the baseboard will fit, based on the height of the wainscoting boards. Any imperfections in the floor will later be covered by the base molding.
Based on these measurements, mark the wall with chalked twine at the point where the top of the MDF baseboard will go.
Rip the MDF into strips 5-1/2 inches wide. Cut the strips to length to fit around the base of the room. Wherever the strips meet along the straight portion of the wall, cut scarf joints so the pieces match up to hide the seam. One piece should be cut at a 15-degree angle to the front and the complementary angle on the back. Join the pieces in the corners with 45-degree angles.
Cut the 4 x 8 sheets of wainscoting in half.
If there are any electrical or cable outlets or phone jacks exposed, measure and mark the location on the piece of wainscoting to make cutouts. Using a drill with a bit large enough to fit a jigsaw blade, drill a hole on the edge of the area to be removed. Be sure to drill within the mark, then cut around the marked area with a jigsaw, starting in the drilled hole.
Liberally apply construction adhesive to the back of a wainscoting panel and hold up to the wall so the beading runs vertically.
Quickly tack the wainscoting down with 2-inch brad nails to keep them flat against the wall and prevent them from shifting.
After putting up the wainscoting, tack the base molding to the outside of the MDF at the base with 2-inch brad nails. Be sure the molding also has scarf joints to hide the seams.