Remove decorations, pictures and nails from the wall. Pull off the old moldings and baseboards, using a crowbar. Sweep the walls down with a clean broom and wash lightly with a damp rag. Let the wall dry completely.
Create a zigzag pattern on the back of the paneling with construction adhesive. Circle the outer edge of the panel with the glue. Do not apply the adhesive right next to the edge, since this might cause an extra mess.
Place the panel in one of the corners with the glue side towards the wall. Apply pressure in the center of the panel and push towards the edges. This pushes out any air bubbles behind the panel.
Secure the paneling to the wall with finishing nails and a nail gun. Keep the nails around the outer edge to hold the oak plywood paneling in place while the adhesive dries.
Cut paneling pieces with a jigsaw for areas around the doors and windows that do not take a full wall panel. Finish installing the paneling by matching the pattern on adjoining panels as closely as possible. Once the adhesive is dry, install chair rails, decorative caps and baseboards.