turn it off !
The first thing to do is turn off the alternator as if it is the regulator that has failed and it might we be that the alternator is putting unregulated current into the battery this may well start a fire if left long enough , but it will destroy the battery in a very short time .
Another reason for switching off is to conserve battery power as in the case of a belt falure the regulator will sence this as an under voltage and put as much power as it can into the alternator field to compensate , this will have no effect what so ever on the alternator output if it is not turning but it will drain the battery much quicker.
The failure that started this thread sounds like a bearing failure in the alternator, this can sometimes be picked up before the alternator fails compleatly , the tell tail clue is intermitant and very short term low volts warnings , this is the result of the brushes not contacting the rotor as the rotor bearings are starting to fail.
It takes about 10 min to check the alternator for play in the bearings and if it is not that about another 10 min to change the brushes if they are worn out.
In the case of a major mechanical failure of the alternator it must be switched off to prevent the risk of an eletrical fire , it is quite likely that the belt will break in this case and the belt is likely to end up resting on a hot part of the engine and giving off a smell of burning rubber.
This smell is most worrying when you are in the air , but I have yet to see a belt catch fire.