For instance, how would you hook up a electric pump communicate with a motherboard? Let's say I buy a electric pump, I hook it up to some sort of metal structure that if the pump is turned on it moves the metal structure, how would I hook up the pump to my motherboard so that I can program it?
Ok, It sounds like you either saw an arm with hydraulic actuators or a Hollywood special-effects movie (they really like hoses in their robots).
Assuming you saw real hydraulic actuators, then I need to start by saying that is only cost effective if you need a lot of force. The majority of robots use electric actuators, specifically servo motors.
Hydraulic actuators work by controlling valves, not the pump. There is typically just a single pump that maintains a very high fluid pressure in a reservoir, called the "accumulator". The accumulator is like a battery of hydraulic energy for the actuators, and the pump just keeps the accumulator "charged".
The control of the actuators is done by "proportional valves". The servo controller regulates the amount of fluid passing to the actuators by controlling these valves, based on feedback from position-sensors in the actuators. A central computer is often tasked with commanding the servo controllers, but that's often not necessary. Sometimes the servo controllers are commanded by some form of hand control.
So you might already see why most robots use electric motors instead of hydraulics. Hydraulics add more layers of complexity to the robot. Electric motors are more direct if you don't need the power that hydraulics provide.
By the way, it's possible that you've mistaken cables for hoses. Often, the motors are placed away from the joints and "tendons" are strung through the arm to connect the joint to the motor. Occasionally, these tendons might be hydraulic hoses.