I understand that Death comes out when a player rolls a one but after that who rolls for death for his movement? Does each player roll when its his turn or does Death have to wait his turn like everyone else?

When you as a player roll a "1" for your character, after you are finished with your characters turn, you now roll again for death and move him accordingly.

Next player would play as normal. They would not roll and move death, unless they also rolled a "1" to move.