Wash it gently, never use a brush or strong stream of water on ginseng. Just swish them around in a pan of water and rub the dirt gently with your fingers.
Lay them out on a screen or in a shallow, open cardboard box in a relatively consistently warm spot in your home and they should dry just fine. Keeping fresh airflow is important also.
Generally, depending on size and warmth, it will take at least two - three weeks or so to air dry most lots and longer for larger roots.