I am going to assume you are running the original 2001 alternator. You need a voltmeter.
1st thing to check, with everything off, take the meter and put one lead on the engine block, the other on the large thick output wire, it used to be black with a orange stripe. You should get battery voltage.
2nd. You should have a yellow/white smaller wire. With everything off, this also should have 12v on it at all times.
3rd. There should be a lightgreen/red wire. Keep the meter lead on the engine block ground, and put the other lead on this green/red wire. When you turn the key to run, it should have 12v. Turn the key to off, 0v. This wire brings the alternator online to charge when the key is turned on. Without voltage on this wire, the alternator will not charge. If voltage is on this wire at all times, it will run the battery down.
There is another wire, it's a white jumper wire. It should still be in place.