Mold is made up of tiny spores that, when disturbed, enter the air and move from one place to the next. Those spores that land in a warm, moist area are likely to flourish and grow until they are hard to clean away. Because spores can enter your respiratory system, it's wise to wear protective gear, including gloves and a face mask, to prevent breathing it in.
It's possible to use most types of detergent to clean away mold, especially those marked as mold removers, but for larger problems and more aggressive mold growth, use bleach. Create a solution of ½ cup of bleach to ½ gallon of water. Apply the bleach solution onto the surface of the mold. Allow it to sit and dry thoroughly.
If using a detergent, follow the usage instructions on that product. Then spray the mold or use a towel dampened with the cleaning mixture to wipe away as much mold as you can. Dry the surface completely with a towel once all mold is removed.
An alternative to using bleach or chemical-based cleaners is to use undiluted white vinegar on the window sill itself. Simply apply it and allow it to dry. You can also use a half-and-half solution of water and ammonia in the same way as you would bleach. Spray it on, leave it there for several hours, and then wipe it clean. Don't mix ammonia and bleach products.