There are two simple tests you can perform to determine if your car's alternator is going bad: a headlight test and a battery test. Once you have narrowed down the issue with these tests, you can perform electrical tests on the alternator itself to determine for sure whether it is malfunctioning. Telling whether a car's alternator is going bad is a little tricky. Specifically, it is difficult to distinguish between problems with the alternator and problems with the battery; these problems manifest with similar symptoms, since a broken alternator always leads to a dead battery.
The headlight test is the easiest test to employ, so use it first. Perform it in an outdoor area to avoid carbon monoxide build-up. Start the car and turn on its headlights. Have someone watch the headlights as you press on the accelerator. If the lights dim, it points to the alternator as the cause of the vehicle's issues. On the other hand, if they stay bright for the duration of the test, your alternator is probably functioning well.
Next, perform a battery test. Open the hood of your car, and start it. Once the engine is running, disconnect the negative (black) cable on your vehicle. It helps to loosen the cable's bolt first to make it easier to remove. If the engine stalls or stops when you remove the negative cable, it is a sign that your alternator is not generating sufficient electricity to keep your car's engine running.
If either of these tests points toward your alternator as the source of the problem, it is worth having a definitive electrical test done to know for sure whether a replacement is necessary. Since the alternator must first be removed to perform an electrical test, most mechanics charge a fee to do it, but if you are mechanically inclined, you can remove your car's alternator on your own, at which point most auto parts stores are happy to perform an electrical test for free. Typically, the alternator is much easier to remove for testing in overhead valve engines because it is located near the top of the serpentine belt.