First of all, is the battery truly dead or do you just have a poor connection? Make sure all battery cables are clean and tight (both at the battery and at the other ends.) Also, it is possible the battery just went bad, but that's not as likely.
Usually, a voltage reading is done with the meter connected in parallel and a current reading is done with the meter connected in series...assuming your meter can be set to measure current, I would use it this way instead: Adjust the meter for amps (you usually have to plug the leads into the meter differently), disconnect the positive battery cable, and connect the meter in series between the positive battery terminal and the positive cable. With a good electrical system, if you have a modern stereo (one with a memory in it) or a working dash clock, it will read a slight current, maybe 50 milliamps or less. If you don't have either of these items it should read zero or nearly so.
If you read a higher current, there is a shorted wire or maybe a trunk light stuck on, something like that. It could have been as simple as leaving the door ajar overnight and the dome light ran the battery down. Like Wrench Bender said, start pulling fuses one at a time until the reading drops to zero and that's the circuit with the problem.
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