Mix 2 tbsp. liquid laundry detergent with 1 gallon of water in your bucket. Dip a broom in the water and scrub the surface of the deck to remove dirt and debris. Use a scrub brush to scrub the recesses of the cracked wood. Spray the deck thoroughly with water from a garden hose to remove the soap residue. You can also clean the deck with a commercially available deck cleaner. Let the deck dry completely.
Remove loose pieces of splintered wood from the cracks by hand.
Mix two-part epoxy wood-filler according to the manufacturer's directions. Use a putty knife to blend equal amounts of the two parts of the putty kit to create a moldable, clay-like consistency.
Press epoxy filler into the cracks with a putty knife and build up the epoxy filler so it sits just above the deck's surface. Let the epoxy filler dry until it is hard.
Sand the surface of the epoxy with 100-grit sandpaper until it is smooth and level with the rest of the deck. Sweep up the sanding dust and discard it.