The voltage regulator is sitting between B & D and is trying to regulate the voltage on the output, from the Input to the Output. A & C are simply the common ground. I'm suprised there aren't one or two capacitors on the board as well (most regulators need them). Don't be confused by the vary resistance from A-B & C-D, that's just the regulator trying to operate outside of specs.
What you need to do is identify which pair of pins are the input, apply the proper power, and then measure the voltage on the out pair.
What you need to do is identify which pair of pins are the input, apply the proper power, and then measure the voltage on the out pair.