You would pull the positive post from the car battery while the car is running and if the car shuts off then the alternator is bad. You can do this in your drive way.
If your car starts having problems suddenly, and then starts running on battery power until the car dies, your alternator is dead. You'll know because the battery will keep going.
The easiest way is to take down to your local auto-parts store. I believe Advance Autoparts as well as Autozone will run a test on it for free. Have them also check your battery while your at it.
