Most Auto Supply Stores should be able to check the Alternator for you, usually free of charge. This is not always 100% though. I recently had an Alternator checked and tested good. When I disassembled it, I found that there was an entire Diode missing from the Diode Pack.
Checking the Diodes is easy if you have a Digital Multimeter with a Diode Check Option, if it doesn't, using the Ohm's setting will work also. A good Diode will read around .400 - .500 when measured in one direction and show open when measured in the opposite direction. If you receive a low reading in both directions or an open in both directions, that particular Diode is bad.
The Stator could be at fault as well as the Rotor; both aren't difficult to check. Look for any obvious areas of wire darkening, this may be an indication of a short induced hot spot; not usually the issue unless the Alternator is very old. Look for any melted tape around the Rotor Windings or Resin that has peeled away from the Stator Wire. Also check all the Solder Connections for poor or cracked Solder Joints.
Be sure to look at the Brushes for damage or wear and inspect the Rotors Copper Slip Rings for gouges that may have been caused by damaged Brushes and make sure that the nuts, bolts and screws are tight.
There may also be a Radio Suppression Capacitor inside, check that as well; it should read as an open circuit.
While you have it apart check the Rear and Forward Bearings; they should be silent when turned by hand; you'll have to check the Rear Bearing by turning the Rotor Shaft manually. Any noise or sloppiness requires replacement; they're easy to find.
Have you checked the Voltage Regulator and the external Alternator connections?
The photo is of a 1965-1966 Alternator.
Hope this is of help.
Ray
