Move the wood outside in the sun if possible. For fixed wood, increase air circulation with a fan. Add a heater to the room if temperatures are cool to speed the drying. Proceed with treatment after the wood is dry.
Scrape off any topical mold if the piece of wood is unfinished. Remove the paint or varnish on coated pieces with a remover formulated for whichever coating is on the wood. Use gloves when applying chemicals.
Spray or paint the solution on the wood surface and allow it to work for the time recommended on the product. Scrape off the finish after it bubbles up. Put newspaper on the ground to catch the debris.
Mix a solution of 8 to 10 tbsps. trisodium phosphate and 1 cup of chlorine bleach in 1 gal. of water. Use your gloves and rub the solution into the moldy wood. Use a scrub brush to penetrate the grain.
Rinse the wood completely. Let it dry in the sun or use the fan and heater to dry out the grain. Sand the piece when it is completely dry to remove burrs and smooth the grain. Refinish it with a mold/mildew-resistant paint or synthetic sealant if you wish.