Spray the wood plaque with a light coating of spray varnish. Allow the varnish to dry.
Rough up the surface of the varnish on the front of the plaque by rubbing it with fine sandpaper. Do this only on the position where you will affix the poster.
Add a thin coat of spray adhesive to the front of the plaque. Spread the poster over the adhesive. Smooth the surface of the paper with your hands, removing any creases or bubbles by lifting up the corners and pulling them out gently until the entire surface is one smooth expanse. Allow the adhesive to dry.
Cover the entire plaque with another coating of spray varnish. Allow the varnish to set overnight before hanging the poster.