In order for mold to thrive, it must have oxygen, a food source, the correct temperature range and moisture. Remove these aspects from the environment, and the mold spores cannot reproduce. Some of these conditions will be out of your control, but by removing any one of them, mold will not be able to exist. The best bet is to remove the moisture or the food source. Vinyl floors often have grooves, which provide a hiding spot for food sources, and mold spores can propagate from something as small as an abundance of dead cells.
Mix 2 tbsp. of chlorine bleach with 1 quart of warm water. Pour some of the mixture into a spray bottle.
Spray the moldy area of the vinyl floor lightly with the chlorine bleach mixture. This with dampen the mold spores and stop them from becoming airborne during the cleanup process.
Don the plastic gloves. Wear clothing that you can immediately place into the wash after cleanup.
Dip a scrub brush into the bleach mixture, and scrub the mold. This may require a little elbow grease, but it is important to get as much of the mold removed as possible. Don't worry about scratching the vinyl. The bristles of a scrub brush are not hard enough to damage the vinyl flooring. If the floor had a finish on it, the mold has already destroyed it. Use a towel to do a quick cleanup of mold residue when you are finished.
Rinse the vinyl floor with warm water. If the mold is gone, then you are finished. If it is not, then repeat the process.
Mop the floor thoroughly. Place your clothing, the towel and mop head (if possible) into the clothes washer. Rinse out the scrub brush thoroughly or throw it away.