Sadly, the only test the average car owner can do is to switch on the air conditioning system to see if it works- or not.
In practice, regular service and repairs on modern air conditioning systems can only be done by suitably certified mechanics. This is not because air conditioning systems are complicated. It is because all air conditioning refrigerants are harmful to the atmosphere, although modern refrigerants are less harmful than older types.
Therefore, only suitably certified technicians are legally allowed to perform car air conditioning repairs. Moreover, most modern car air conditioning systems are controlled by computers. This means that the air conditioning systems on most cars can only be diagnosed with diagnostic computers. So how would a technician test an air conditioning system that does not work?
This largely depends on the nature of the problem, but here is what a technician will typically do-
Note that the above steps describe a general overview of A/C system diagnostics. The actual car air conditioning repair steps any technician takes depend on both vehicle make and model, and the nature of the failure.