how to measure battery
Hi
There are some "battery testers" in the market which are mainly composed by 2 circuits. 1) The battery current capacity which is applies a load while measuring voltage and amperage. the load should be applied for short time lets say less than 1 min, then release it, wait a few minutes and apply the load again, if the battery can recover its nominal voltage (~12vdc) and during the measuments provided high current (I dont remember how many) then the battery is concluded to be capable of retaining charge. The ph of the acid is also meassured by other simple instrument.
About the charging system, you can use an analog voltmeter and measure at the battery poles while the engine is runing, it usually reaches 14 or 15 vdc. It means the car charging system is working.
cheers
Sal