If it's the battery then the test for this is easy.
Charge it up and do a discharge test, you will need a battery discharger tester for it, or ALL garages should have one.
The DIY method for this is to charge it up then turn the headlights on full. They should stay illuminated for several hours, if that doesn't happen then it's a battery problem.
If it's a modern vehicle then if no charge is going to the battery then a dash light should show up.
If the battery is self discharging then clean off the terminals and the earth lead onto the vehicle body.
The above are just diy basic tests, of course the problem with modern vehicles could be a bit harder to find with all the electrically operated systems.