It is a simple matter to check if the alternator is charging.
....Use a voltmeter at the battery and look at the voltage just after starting.
....Since cranking has taken charge out of the battery, it will have to be recharged after the motor starts, as sensed by the regulator.
....What you should see is about 15 volts +, then it should taper down to 14 or less in a few minutes, with a new battery in place.
....I assume your battery charge lamp is on?
....Here is how the charge lamp is controlled, telling you either the alternator is charging or not.
....The charge lamp has battery voltage applied to it through the ignition switch as soon as you turn on the switch.
....It gets it's ground from the regulator, to light up when the alternator is 'not' turning at idle speeds or faster.
....As soon as the alternator output comes up, the regulator removes ground from the lamp putting it out, as an indication the alternator is outputting.
....There is not much to the whole circuit besides harness, plugup and fuses..
.....What conditions do you have?
....Is the belt on the pulley? Just making sure!