Batteries are tested using a drop/load tester.
A Drop/Load tester- creates a load on a battery, you read the voltage before, during and after. If you have fully charged battery meaning on a (12volt battery) you have 12 volts or better, you load the battery at half of the rated cranking amps for 15 seconds, the volts should not drop below 9.6 volts during the test and the volts should recover within 15 seconds to above 12 volts after the load has been removed. If it doesnt then check the levels and specific gravity of the acid in the cells and if all is correct and it still fails the drop test then it generally means one or more of the plates in the battery cells has warped or corroded and the battery is dud.
As above you should ideally have a matching pair of batteries of the same make, ratings and age otherwise you will generally find one battery tries to discharge the other.