By the time of the creation of the Daleks, Davros only had the use of his right hand, which he used to operate controls on his chair. These could perform functions for controlling doors, the Mark III travel machines, or his own life support system. (TV: Genesis of the Daleks)
On Necros, Bostock fired a gun which destroyed most of his right hand and with it his ability to operate independently. (TV: Revelation of the Daleks) For a short time after, his hand was replaced with a claw (COMIC: Emperor of the Daleks!) and finally with a prosthetic substitute. (AUDIO: The Juggernauts, The Trials of a Time Lord, TV: The Stolen Earth/Journey's End, The Magician's Apprentice/The Witch's Familiar)