The electrical system in most modern cars is a complicated menagerie requiring specific knowledge and expertise for many repairs.
These systems control a lot of the functions and systems in the vehicle from the engine to the fuel system to the air conditioning to safety features to your entertainment system. Wiring, circuits, relays, computers, and more are all working together to run everything on your vehicle.
Diagnosing Electrical Problems
Many problems will trigger the engine light (another electrical system) by giving an error code to the car's computer. These can be diagnosed simply by plugging in a computer to the vehicle's interface and finding out what the code is and what it means. Kits for plugging into the systems of most vehicles can be purchased at auto parts stores as well as interfaces and apps for smart phones and laptops.
If your vehicle won't start, then begin diagnostics by looking at the most obvious items first (battery, battery cables, etc) and working your way outwards to the more complex, individual systems.
Total Electrical System Failure
This is relatively rare, as usually it's a failure of the battery or alternator producing power or of an individual (but vital) system failing and causing the rest to no longer function. The car's security alarm, for instance, could fail and make it impossible to start the car at the keyswitch until an override is made.
There are many ways to diagnose and repair or work around (until a fix is found) most electrical system problems.