On most cars all you have to do is unhook the positive side of the battery when the car is running. If it dies the alternator is not working. If it is not working your battery will just run out of juice, no light, no start.
Check the voltage at the battery, you can do it with the lights on to see if it holds under load. DO NOT REMOVE THE CABLES WHILE THE ENGINE IS RUNNING! This worked on older cars but ones with computers are sensitive to voltage spikes wich you will get if you remove a cable while its running.