How do you know if a starter relay switch is bad?

Take it to a mechanic to test the battery, charging system, and starting system (both the solenoid and starter if they are separate pieces). Or remove the starter and take it to a parts store to have it tested. If the battery is ok, the alternator/charger system is putting out power, and you think the starter or solenoid is still the cause, unhook the ground from the battery post after the car has been running but is turned off and leave it like that till the next time you turn on the car when you'll screw it back on. If it starts no problem then it's probable it's the starter or solenoid that was sucking the battery dry.