Clear away any foliage covering the fence and move lawn furniture a safe distance away. Clear the area of children and pets. Put on sturdy, close-toe shoes.
Connect a power washer to an outdoor water supply, and attach a tip with a spray pattern between 15 and 40 degrees Fahrenheit. Use a white 40-degree tip for superficial dirt, and a green 25-degree or yellow 15-degree tip for deeper cleaning. Avoid the red 0-degree tip -- it can gouge the wood.
Start the power washer and clean the wood by moving the tip along the grain. Keep the tip at least 6 inches from the wood to avoid splintering or gouging it.
Wash the fence with a solution of water and a commercial exterior wood bleach that contains oxalic acid. Wear gloves. The bleach removes dark tannin stains and iron oxide stains from nails without changing the natural color of the wood. Apply the bleach with a sponge or paintbrush and let it soak in, then wash it off with the power washer, using a white tip.
Let the wood dry for one or two days. Apply a semitransparent stain with a paintbrush. Make sure the stain contains a mildewcide to prevent blackening from mold, and use a stain that matches the natural wood color for best effect.