My instructor has me set the whip on top of the rein with first 3 fingers closed over, thumb and pinky on the other side and then it lays across my leg, same position for my hand as if it was empty.
I have to hold it at the very end of the handle but she has me using a shorter one I believe.
To change, put both hands together (whip should be straight up and down now), grab both reins with the hand currently holding the whip, pull the whip up and then down with the empty hand.
Oh and practice changing before you attempt it while riding, the first time I tried changing while at a trot, I got all tangled up and bopped the horse in the head. Thank God for non-spooky, calm, complacent Warmbloods, all he did was give me a dirty look of "What did you do that for!?"