The manipulator arm is the long, thin, mechanical arm usually found on most Dalek models, the exceptions being some Dalek Emperors' models and the Special Weapons Dalek-type model.
It is usually found in the right-hand socket in the Dalek mid-section, with the gunstick on the left, however some of the black-domed Daleks within the Dalek Imperial fleet in the year 200,100 had it the other way round. (DW: The Parting of the Ways)
Types
Plunger
The ends of the manipulator arms typically are shaped like a plunger. For this reason, Dalek technology often has circular controls with which some can arm an interface by rotating clockwise or counter-clockwise. However, the black tip at the end, which gives the arm its "plunger" shape, can morph slightly to better interact with specific objects (such as finding the combination of electronically-locked doors). (DW: Dalek)
Even the Dalek dies, its arm can still operate machinery if used by a live person (DW: Remembrance of the Daleks). The arm can optionally have a telescopic feature to enable the arm to extend outward. (DW: The Dalek Invasion of Earth, Dalek)
It could also serve as a weapon. Placed over the nose and mouth, the arm can generate enough hydraulic suction to suffocate and kill a Human and enough traction to more than crush a human skull or rip through sheet metal. (DW: Dalek, TDA: I am a Dalek)
At least in the case of the Cult of Skaro, the arm could also scan brainwaves for information or as a quick intelligence scan. (DW: Doomsday, Daleks in Manhattan)
Claw
Alternatively, the arm can terminate in a simple mechanical claw with two or three pincers. A variation of that claw had eight pincers and was used to operate Dalek machinery.(DW: The Stolen Earth)
Combination
One of the members of the Cult of Skaro exhibited a combination of the two forms, as a plunger which also had a claw. The claw was in this case used to hold a syringe. (DW: Daleks in Manhattan)
Blowtorch
Some Daleks had a claw and blowtorch combination. (DW: The Parting of the Ways); (DW: The Daleks)
Alternative weapon
The alternative weapon was only seen on two Daleks guarding the Dalek Emperor. It looked like an upgraded Dalek ray gun, but slightly larger.(DW: The Parting of the Ways) Also, Davros' Crucible Daleks were equipped with lockpicks. (DW:The Stolen Earth, Journey's End)