Wait at least three days after washing the deck to sand the surface. You'll need the deck to be completely dry to ensure that all the fuzzy wood fibers are standing from the deck's surface, ready for removal.
Attach 80-grit sandpaper to a random orbital sander.
Put on work gloves, safety goggles, and a face mask before you begin sanding, to protect yourself from splinters and dust particles.
Start in a corner farthest from the steps or entrance to the deck. Turn on the sander, and begin moving it down each deck plank in small circles.
Move at a moderate speed, removing the standing fibers, but not remaining in place long enough to remove a layer of wood from the plank.
Move to the next plank and continue the process, going from plank to plank until no trace of fuzziness remains.
Switch to a sanding block and 80-grit sandpaper to sand away the fuzziness in any hard-to-reach areas, such as around railing posts.
Sweep away the sawdust left from the sanding process with a stiff-bristled broom.