Since I had DS, I've had very dry skin on my hands, especially on my knuckles.
I use an ego QV had wash, no soap (this will dry your skin out more) and QV cream afterwards. Depending how dry they are I put the cream on in between washes as well.

I had to keep them out of water as much as possible, not easy with all the hand washing that goes on with a newborn, but this settled down after a few months and its fine now.