A good tip is to keep a bottle of moisturizer next to the sink or you can carry it with you when you are going for a hand wash and as soon as you have washed and dried your hands, dab a little into your hands and work down towards the fingers.
Make sure that when you wash, that you use lukewarm water only as hot water strips the skin of essential oils.
Use your pure and simple soap to wash with and when you have finished washing your hands, blot them instead of rubbing. Vigorous rubbing to constantly wet hands can cause tiny little tears in the skin that can make them rough and chapped.