I test batteries for a living, well I do other things too but that's one of the things I do.
Do you have a meter? If so get me the following readings.
With the battery not connected, what is the voltage on the battery terminals? (this is to see if the battery is fully charged)
With the battery connected, but nothing turned on in the car, what is the voltage on the battery terminals? (looking for a drain in the electrical system)
With the engine not running and the headlights on, what is the voltage on the battery terminals? (load test of the battery, light load)
With the engine running and nothing else turned on, what is the voltage on the battery terminals? (checking the charging system)
With the engine running and the headlights on, what is the voltage on the battery terminals? (checking the charging system with more load)
With the engine OFF and the ignition disabled, crank the engine over, what is the voltage on the battery terminals? (maximum load test on the battery)
When using a charger to charge the battery the charging voltage has to be above 6.44V, so you can hook your charger to the battery and measure that as well.