How do you know when an alternator go out in a 99 ford crown vic?

By " go out " do you mean not charging? If this is the question, and you don't have any tools, find a small volt meter for 12 volt d/c and connect to the the battery. Should read 14.something volts. If not, and is say 12.2 volts or below 13 volts, then change the alt. But of course, if the lites are dim, and the battery is dead or very low, that might be a sign.