Re: charging system problems
You could try a parasitic draw test; this is to see if anything is drawing current when it shouldn't be (i.e. with the ignition off). To do so set your multimeter to current mode, dissconnect the positive battery terminal, connect one lead of the multimeter to the positive terminal on the battery and the other to the positive lead. You will need to connect the positive test lead on your multimeter to the current test port (which is usually the left one) and set the current range to the highest value, also do not turn on the ignition with the multimeter connected.
http://www.youtube.com/watch?v=KF1gijj03_0
Re: charging system problems
How old is the battery? Does it have enough electrolyte?
What voltage reading do you get on the battery poles when the engine is running? If it's more than ~13V, everything with the charging should be OK, so I would try with a new battery.
Re: charging system problems
The charging voltage should be just over 14v, if it's any less then the carging system is probably at fault. Ideally the battery should be at 12.6 while the engine is off, if the charging system is outputting the correct voltage and the battery voltage dosen't get close to 12.6 and/or the voltage quickly drops off the battery is probably dead.