Battery is being drained overnight

[68_Step]

The 78 Chevy C-30 I just got is eating batteries. Something is draining them completely in a day. I have checked the obvious stuff, radio and all lights are turned off. Could an electrical short be killing the battery? The battery that came in it was dead Saturday morning, so I thought I may have left something on. I recharged the battery and Sunday morning it was dead again. I replaced it with a known good battery Sunday evening and tonight (MOnday evening) it is dead too.

How do I trace an electrical short? Will I need a multimeter? If so, will something I pick up at Radio Shack be ok? Any advice would be greatly appreciated. The truck is new to me so I do not have a past history of electrical problems...