Measure the length of the brick wall along its base, using a tape measure.
Mark the measured length on a strip of baseboard, using a piece of chalk. Cut the baseboard along the marked line with a table saw. Make a 45-degree angled cut in one end of the board if you intend to place it in a corner adjacent to a board along the base of an adjoining wall. Make the angle along one of the boards extend inward from the rear of the board, and the adjacent board extend outward so that they fit tightly together in the meeting corner.
Cover the rear of the baseboard with construction adhesive. Use a notched trowel to apply the adhesive in a layer along the baseboard length. Tilt the trowel 45 degrees and drag the notches on the edge over the adhesive to create ridges in the adhesive surface.
Mount the board against the brick wall, starting in the corner with the angled area and running along the base of the wall to the wall's end. Press the board firmly to the wall, allowing the adhesive to bind the board into place. Mount the adjacent board in the corner with the angled edge against the first. Allow the adhesive to set overnight to secure the board in place.