Measure the area carefully and order wood paneling from a cabinet maker or carpenter. Be sure to tell the cabinet maker that you will be installing the panels over brick walls. The manufacturer will provide you with spaces on the back sides of the panels for mounting cleats. Mounting cleats are solid pieces of wood that install directly to the brick. The panels are then attached to the cleat.
Measure the indentations on the back of the panels. Measure the distance from the top and both sides for each of these pieces.
Cut mounting cleats to fit your measurements. Use 2-by-4 lumber and trim it so that it will fit snugly inside the spaces.
Position the mounting cleats on the wall. Drill a hole through the cleat and the brick. Use a masonry drill bit. A regular bit will be ruined by the brick. Slide a concrete anchor into the hole in the brick. Insert concrete screws through the mounting cleat and into the brick.
Position the panels over the mounting cleats. Attach the panels to the wall by hammering a nail through the panel and into the cleat. Use finish nails to minimize the damage done to the panels. Space the nails 6 to 8 inches apart. Fill nail holes with wood putty.