Cover any adjacent grass or other plants with plastic sheeting weighted down with rocks or bricks.
Hose the moldy areas of the sidewalk down with a hose to thoroughly moisten them. The moisture will prevent the black mold spores from becoming airborne and spreading.
Mix a solution of 1 gallon of water and 4 tablespoons of liquid dish-washing detergent.
Pour the solution onto the affected area of the concrete. Cover even mold-adjacent areas (at least 2 feet on each side of the visible mold) as they may harbor invisible spores. Apply enough of the solution to soak and saturate the concrete but not enough to create a spill-over that may soak into the nearby soil.
Scrub the concrete thoroughly with a long-handle scrub brush.
Rinse the sidewalk with a spray from the hose. Aim the hose away from any nearby soil and plant life so that the solution drains onto the street.
Repeat Steps 4 through 6 if you find you have missed spots.
Mix 1 gallon of water and 1 cup of bleach in a fresh bucket.
Pour it over the washed area following the instructions in Step 4.
Scrub the concrete thoroughly with a long-handle scrub brush.
Rinse the sidewalk with a spray from the hose. Aim the hose away from any nearby soil and plant life so that the solution drains onto the street.