Spray the wood with an all-purpose wood cleanser and wipe it down. This removes any dirt or dust that prevents the wood from forming a strong bond.
Rub the edge of a 100-grit sanding block against the area of the furniture where the wood trim will go. This eliminates some of the slipperiness of the glossy wood. Wipe down the wood with a tack cloth to remove the dust from sanding.
Apply a thin line of carpenter's wood glue to the back of the wood trim. Firmly press it against the furniture along the sanded edge. Wipe away any excess glue that oozes out with a damp sponge.
Attach a metal C-clamp to the furniture and trim to encourage a strong bond. Keep the clamp there for 12 hours.