the easiest way to check an alternator is to take a voltage reading at the battery with the engine running. you should see at least 14 volts present. if you rutn on some accessories like the heater an and rear defogger if the alternator is wrth a damn it should still be able to maintain almost 14 volts at idle. if you read anything close to 12 volts with the engine running your alternator is not doing jack.
pulling the positive terminal off the batter with the endgine running is a bad idea. without the reference voltage of the battery present you couls easily spike the voltage of the car well about 16 volts. not good for your ECU