Apply painter's tape to the wall at the point where it meets the wainscoting panels.
Place a dropcloth on the floor. Tape it to the floor, right at the point where the floor meets the wainscoting panels.
Don a protective face mask and goggles.
Sand the flat, ungrooved portions of panel with a random orbital sander or sanding block.
Sand the grooves and crevices by hand. Sand in the direction of the grooves to avoid damaging the carvings.
Wipe down the wainscoting panels with a damp lint-free cloth to remove dust and debris.
Apply 1 to 2 coats of primer with a paint roller and use a special edging roller to apply primer to the top and bottom of the panel. Allow the coats to dry between applications.
Apply 2 coats of indoor paint. Use the edging roller to paint the edges of the panels at the point where they meet the wall and floor. Apply thin, even coats and monitor for drips, which commonly occur when paint accumulates in the crevices and grooves.