A leather desk is a classic choice of quality and timeless beauty but can quickly go downhill if the leather isn't cared for in the proper way. Owning leather furniture is similar to caring for a plant--they certainly brighten up your life and bring beauty into it but you must treat them responsibly in return.
With a damp cloth, gently wipe the leather of any dust and debris. Make sure to get in the cracks where the leather meets the wood.
Wet your cloth with a small amount of leather cleaner specifically made for the type of leather of your desk or, alternately, rubbing alcohol.
Gently wipe the desk with the damp rag in circular motions, careful to cover every spot.
Seal with a natural oil, such as olive oil or a product made for oiling leather. Using a dry cloth, rub the oil into the leather using the same circular motions as before. Let dry at least 24 hours.