The job of the regulator is to control power to the field electromagnet. When 12V is fed to the field coil, via the white wire output of the regulator, it produces a strong magnetic field that can be checked very simply with some bolts; with the key on, bolts should stick to the 3 screws on the alternator cover. If they don't, you have a regulator or field coil problem. With the black meter lead connected to battery -, and the red meter lead connected to the white reg wire, you should read 12V with the key on. If not, and there is 12v at the black reg wire, the reg is at fault. (All measurements are with the wires connected to the reg.)
Some of the cheap reg/rects may need to have the metal body grounded with an added wire from the body to a good frame ground, while higher priced units may not.