A basic test is straight forward. Grab a pocket multi meter, set it for V DC and start the engine. Hook the meter onto the battery. If you're getting voltage over 13 volts and it slowly climbs til it reaches 13.6 - 14.1 then the alternator is good. If it is only showing 12.X volts and doesn't maintain voltage, the alternator is dead. Buy an old school hydrometer (the glass turkey baster looking thing that nobody uses anymore) to test the battery's condition as well. They are easy to use and will show you if you have a dead cell in a battery.