Fill a glass or bowl with white vinegar, and place it in your dishwasher.
Run the dishwasher through its regular cycle.
Wet a nylon scrub pad with white vinegar, and use it to wipe down the inside of your dishwasher.
Wet a toothbrush with white vinegar, and use it to scrub the limescale off of any areas that are hard to access with the pad.
Mix 1 tablespoon of baking soda with 1 tablespoon of white vinegar to create a cleaning paste for especially stubborn deposits. Dip a cloth into the mixture, and use it to rub off deposits. The baking soda acts as a mild abrasive, which helps to remove particles clinging to the surfaces of your dishwasher.