Ventilate the bathroom and wear gloves and a mask
Mix equal parts white vinegar and water in a spray bottle
Spray the moldy caulking thoroughly
Let it sit for 30 to 60 minutes
Scrub the caulking with a soft brush or old toothbrush
Rinse with warm water and wipe dry
For stubborn mold, apply a paste of baking soda and water
Scrub gently and rinse again
Use hydrogen peroxide on remaining stains if needed
Dry the shower completely after cleaning
Replace the caulking if mold remains deep in the seal
Keep the shower dry and ventilated to prevent regrowth