Open all the doors and windows into the moldy area. Activate the exhaust fan, if there is one. If there is not, set up a fan to improve ventilation. You want a good flow of air to blow out any spores released during the cleaning, as this will help prevent a recurrence of black mold.
Put on rubber gloves and a respirator mask. Safety goggles are a good idea, but only necessary if you will be putting bleach in an overhead area (because of the increased risk of it getting into your eyes).
Make a disinfecting, mold-killing solution of 1 cup of household bleach for every gallon of water.
Scrub the area infected with black mold using a stiff-bristled plastic brush and the bleach-and-water mixture. Let that sit for about five minutes after scrubbing.
Wipe the scum of bleach-and-mold up with an old rag.