Dalek puppets were beings who had been taken by the Daleks and partially converted to serve them as slaves. These slaves were used as sleeper agents. When activated, they would have a miniature Dalek Eyestalk extend from their forehead and a miniature Dalek gunstick from his or her hand.
The process occurred when any unprotected non-Dalek entered the Dalek Asylum; the air contained a nanocloud that would slowly convert the victim into an unwitting servant of the Daleks. Not even death could protect them from this fate: the conversion process worked on dead and living flesh alike, and could turn innocent corpses into shambling, zombie-like creatures. Time Lords cannot be converted by this means. All intact bodies of the Alaska had this fate befall them, apart from Oswin Oswald who was entirely converted to a Dalek. (TV: Asylum of the Daleks)
More primitive progenitors of the Dalek puppets were the Robomen who were prisoners on whose brains the Daleks operated in a surgical procedure called the Transfer, fitting them with large, helmet-like headsets. The Daleks' mind control technique was unstable, and the Robomen would eventually go insane and commit suicide. (TV: The Dalek Invasion of Earth) The eyestalk extending from Dalek puppets' foreheads made them visually reminiscent of Dalek Troopers. (TV: Resurrection of the Daleks)