The electronic control unit, or ECU, is the brain of the fuel injection system. It is a silver-colored box, mounted in various locations on different models. One way to find it is to follow the fuel injection wiring harness as all wires lead to the control unit (terminating in a large plug on the unit). In the Vanagon, the ECU is mounted in the engine compartment on the right side, close to the right taillight assembly. In the Bus, it's mounted in the engine compartment, immediately forward of the battery. In the Beetle and Super Beetle, it's mounted in the rear luggage compartment.
The ECU processes all the inputs from the various sensors on board and uses that information to determine the optimum amount of fuel to be injected, which it controls by varying the amount of time the fuel injectors are open.
The ECU cannot be electrically tested. The ECU should only be assumed faulty if absolutely everything else in the ignition system, fuel system, and fuel injection system has proven to be working properly.