How to do you read the alternator gauge?

The VERY FIRST thing you need to do is get the car running and clip a voltmeter direct to the battery. Increase RPM to simulate cruising speed and see what the meter reads. If it's very much above 14, or an absolute limit of "above 15.5" (and that is somewhat high) then the regulator is not properly controlling the voltage.

If the voltage is 14 or lower the battery is "down" (somewhat discharged) or bad. IE defective battery.