Testing the alternator is a easy process. The only tool you will need is a multimeter. This test will also tell you if your positive battery cable is good or bad.
First place your multimeter probes on the battery.
You should get a reading from the battery of about 12.6v
Now start the engine and have it running at about 1500 rpm. You should have a reading between 13.2v and 15.2v
Now while watching the meter, increase the RPM to between 1800 and 2800 RPM. The voltage readings should not change by more then 0.5v.
Now turn on things like lights, radio, anything that will draw power. The voltage should not drop below 13v.
If you have a reading above 16.0 volts on the first test, then the voltage regulator has failed and the alternator is overcharging the battery. This will damage the battery by over charging.
Any readings below 13v on the first test indicates low voltage. This can be caused by corroded cables, clean all of them, slipping belts, check and replace if needed.