If you have a voltmeter installed, a failed alternator will cause it to read ~12V (or ~24V) while a working alternator should show ~14V (or ~28V)
The voltage regulator (wired in after the alternator) outputs a voltage higher than the nominal battery voltage so that the battery can charge. If the voltmeter reads the nominal battery voltage it may indicate a failed alternator. It can also indicate a bad voltage regulator.
Depending on the type of ammeter you’re aircraft is equipped with it may show discharge vs charge current in which case a discharge indication could indicate a failed alternator or an alternator that can no longer supply the required current to operate all of your electronics and you are operating at a loss.