If the alternator has an AVR and rotor has two slip rings. Then you disconnect the brushes, connect a 12v battery to the brushes, and start the generator. Check for your normal output voltage. If not present then the either the rotor or the fields is bad. If the voltage is present run for a few minutes and shutdown. After shutting it down remove the battery, reconnect the brushes, and then restart the generator provide it was outputting the correct voltage. If now there is no voltage then the AVR is dead.
Now there capacitor driven model out there too.
If needed I can post a link to the Briggs basic generator training manual that has very information on troubleshooting portable generators.
