Start with a simple check of the drive belt. Make sure it's there and tensioned properly. If that's OK move on to the basic volt meter check across the battery terminals. With the engine off, you should see somewhere between 12 and 13 volts. Start the engine hold the RPM near 1000. Return to the battery and measure the voltage again. You should see a 1 to 1.5V increase over what you saw with the engine off. If you see more than 15V, you can assume the problem is probably in the control box. If it has not increased it could be the control box or generator.
You can make a couple of generator measurements in the car. Remove the two wires from the generator. Check each for continuity back to the control box. If they're OK, make up a test jumper. This jumper will go between the two terminals on the back of the generator when the regular wires to the control box are removed. The jumper needs to have a bare spade lug so you can probe it with your volt meter. Start the car and connect your volt meter between the jumper and chassis ground. Note the reading. Have an assistant slowly bring the RPM up to 1000. The voltage should increase steadily but not exceed 20V.
If the meter shows no voltage, examine the brushes for wear. A reading close to 1V indicates a potential problem with the field windings. A reading close to 5V indicates a problem with the armature.
These steps were paraphrased from the AutoBook series of manuals.