Condensation is the cause of damp in many homes. When warm air comes in contact with air lesser in temperature, mist is formed. But what are you going to do if there is excess moisture leading to wet window sills? It is quite obvious in a household, that there will be cooking, people will take bath, clothes be dried and other activities carried out. So, the best solution is to reduce condensation.

You can use dehumidifiers to ward off excess moisture and maintain a steady level of moisture in your home. But before buying one, check out its energy efficiency features.
Extractor fans are a great help in pulling out the steam from kitchen and bathrooms.

It is always better to dry clothes outside home to prevent moisture build up within rooms.

Keeping a bottle of moisture collecting crystals near the window sills also helps in a meager way. This method is not as effective as the dehumidifier but it is cheap.