How do you if alternator is not charging?

Use a DVOM (Digital Volt Ohm Meter) to see how many volts are output at the battery if it 13.3 to 14.4 the alternator is putting out the right voltage.
Now you need to test that it is putting out enough amps, some dvom s have an inductive pick up clamp you can use to read the amps. Otherwise O'reilys, advance, pep boys auto parts will usually test it for free while it is in the car