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The first place I would start is to make sure the belt is still in place. Then I would check the wiring on the back of the alternator.
If all the visual checks look good, I would then use a multi-meter and check the battery with the engine off, then running to see if there is any differences in voltage.
If there is not a difference in voltage, I would pull the alternator and take it to the local auto parts store and have them do a test on it.
After this, it all depends what you find out.
Hope this gets you started in the right direction!