You would attach a screw thread to a motor (using ACME thread - its suited towards driving a mechanism rather than holding a picture on a wall for eg).
The screw thread would have a nut on it, which is fixed to the base of the arm. as the screw thread turns, the base rises and falls.
You could use either a stepper motor, or a Geared DC motor with encoder.
If accuracy is important, then a ball-screw would be needed because these dont have backlash - this is when there is a bit of play in the nut.