Warning Do not ever do this with a late model car with electronic ignition, especially is it has a computer.
Remove the negative cable from the batter with the engine running. If it still runs, the alternator is at least working. To confirm that it is working correctly you must use a voltmeter. A properly functioning alternator should generate about 14.5 volts. If it's a little lower, it may indicate a discharged battery. If it's under 12.5, it's not charging and needs to be replaced. If it's over 15, the regulator is shot and you need to replace it.
It's not a DA "switch", it's a DA plug. It's a plastic plug that goes on to the two small terminals on the edge of the alternator. It has a diode in it, but you can't see that. One wire goes to the BATT terminal on the alternator, and the other wire goes to the + side of the coil or ballast resistor or to the ON terminal on the ignition switch.
The battery and alternator are in the same circuit. So, if the alternator is putting out enough current, the battery will be charged up. What can happen sometimes is that the alternator isn't capable of providing enough current for the entire system (big boom boxes will cause this), so the battery has to supplement the alternator's output. This will cause the battery to discharge.
