Put a meter on the engine battery terminals while the engine is idling and check the voltage with the DC meter. Normal voltage should be around 13.7V or better.

Usually the battery light will indicate the alternator is putting out low voltage. Note that at higher RPMs, the alternator will put out more voltage, so the battery light may go out when you are on the freeway and driving at high RPMs. It also depends on how many accessories you are using since the voltage goes toward the accessories instead of the battery. This includes lights, wipes, fan, heated seats, etc.

If the alternator goes and the battery is full, you'll get maybe 20-30 minutes of drive time before the battery can't sustain normal engine electrical draw, i.e. spark plug and you will ungraciously get stuck and need a tow or another fully charged battery to get you 30 minutes farther.