If you think that's complicated...read the link below. It's written by an Audi guy but we all use pretty much the same Dr. Bosch's magical mystery parts.
http://www.humanspeakers.com/audi/alternator.htmI'd do three quick & painless tests myself:
1. With the motor off test the battery voltage between the terminals. Be careful not to short those terminals together, of course. You should see about 12.5VDC in reasonable temperatures, maybe a little less if the car has run recently. If you don't, get a trickle charger on that battery until it's well above 12VDC.
2. Next, a resistance test (ohms) from the battery negative to the frame. Should be really low, like 0.1 or something negligible. Then head up to the engine bay and do the same test between the intake manifold, ground stud and alternator housing. All should be negligible as well. You might have to scrape the probe a bit to get a good ground. If not, resolve those issues next by cleaning the grounds & lubing with a bit of dielectric grease.
3. Then turn on the motor...verify that the alternator bearings are quiet (no squealing or chirping); the belt is running nice and square with crank pulley and is tensioned properly. You'd be surprised at the number of times I've seen a bent mount arm or worn mount bushings. Any of those will cause the alternator to undercharge.
If all these tests pass, get that battery & alternator to
either one good alternator shop/mechanic or
three auto stores. Auto parts clerks don't know what they're doing sometimes and it really helps to have multiple opinions. Alternators and batteries can only truly be tested in use, load testing is a requirement.