Lay a drop cloth to protect your floors from getting wet during the cleaning and to prevent moisture in the floors from contributing to your mildew problem.
Mix a solution of laundry detergent and warm water in a bucket. Use a capful of detergent for every gallon of water.
Dip a scrub brush into the solution and vigorously clean the baseboard. Scrub any concentrated patches of mildew especially well.
Dry the baseboards thoroughly with clean rags.
Mix 1/8 cup of bleach in a spray bottle with 1 quart of water. Apply a light mist to the baseboard to kill off any remaining mold spores. Color-test the baseboard first in an inconspicuous area if you're concerned about fading the paint. Allow the baseboards to air-dry.