Grab a multimeter and test the voltage at the battery. At idle, it should be 14.5V or so. I get real lazy and go to the autoparts store and let them check it for free.

It is possible that you need a voltage regulator, the brushes wear down and slip out of place. You don't need to buy a new alternator or even remove it from the engine bay.

I drained a little antifreeze and removed the top water pipe to gain access to the back of the alternator. Disconnect the wires, use a phillips to remove the plastic cover and then remove the regulator. A one hour job.

Of course, check the tension of the belt. Just push on the belt.
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Keeping it running is better than buying new