Put a voltmeter to the terminal at the back of the alternator. There should be 12 volts there at all times. If that one's hot and the small red lead is connected to it, you've got a bad alternator. It doesn't matter where it's connected, as long as it is able to put a high current into the battery. Yes, a wire directly to the battery will work, but the ammeter won't indicate a charge if you do it that way.
Jerry