short

put a volt meter on the battery and watch it while you crank. if it drops more than 2 volts, battery no good.

while its running, check voltage at alternator and battery. above 13 volts is charging.

with the negative cable off, put a test light clip on the bat cable and touch the pointer of the test light to the terminal on the battery. if it lights up(make sure all lights are off, doors shut), you have a draw.