check the belt tension on the alternator first, if it is loose the belt will slip and cause this. pay attention to the pulleys also, if it is worn even a new belt will have a problem and may slip.
then get a vom and check the output of the alternator, it should be between 13.2 - 14.8v. If it is any lower then it's either a loose belt or a faulty alternator.
There are also some fuse links in the harness that run under the intake/spark plug area, check those if you do not find anything wrong elsewhere, especially if your vom readings for good alternator output are low or non-existent.
I would perform a load test on the battery too.