It could be several things.
I would check for a short that is killing the battery.
But my first guess would be the alternator. Start the car and put a volt meter on the battery. If the alternator is putting out power it should read somewhere above 13 volts even as high as 14.5 volts. That will tell you that the charging system is working.
(FLL If you buy a volt meter at Walmart you can probably use it once and take it back for a full refund)