How do you test a voltage regulator?

You just need an accurate voltage meter.

Connect the meter to the poles of the battery. Start the engine and avoid spinning her up, even not for a short moment. The reading of the meter now can be anything; a reading lower than 12.6 volt indicates a weak battery.

Slowly increase the engine speed. The meter reading should increase too, but will get "catched" at an engine speed somewhere at 1000 rpm. (8001200) From then on the reading will stay "locked". It should be 13.8V; 0.5V higher or lower is the limit of what is acceptable. A voltage too high is NOT good: it will ruin your battery and wear out bulbs and other equipment!

A voltage regulator is good when the reading hardly reacts to change of engine speed or to adding power consumers like electric window heaters or main headlights.

Ans 2: sometims the voltage regulator is faulty when the remainder of the alternator is OK so it's worth considering replacing the regulator first because it is less expensive and sometimes it can be removed and replaced without taking the alternator off the car.