Just off the top of my head... use voltmeter to test the battery without cables attached. Record voltage. Connect the battery cables and start up car. Check voltage of battery while car is running. Should see a rise in voltage. While car is running, (with a thick heavy glove on your hand), disconnect battery... does car continue to run or does it stop instantly?
Once upon a time, Chilton had in the front of their manuals a fairly straight forward diagnostic chart. Look through it and go step by step.
Theres really not much in the charging system..... battery, regulator, alternator, link, cables, ignition switch, starter..
I had an 67 Mustang that used to constantly kill batteries. I changed out the battery, alternator, cables, ...till I got to the regulator. That was my cause. But go throught the Chiltons diagnostic step by step and see what you find..