The air conditioning, or AC, system is the most complex part of the entire HVAC system, with the most mechanical parts.
It starts at the engine with the air conditioning compressor. This part compresses the refrigerant in the AC system, raising its pressure. The high-pressure refrigerant then passes through the condenser, which is a heat exchanger that is normally mounted in front of the radiator. Inside the condenser, the AC refrigerant turns from a gas into a liquid by shedding heat to the air flowing through it.
From there the refrigerant passes into the evaporator, which is mounted inside your vehicle along with the heater core. In the evaporator, the refrigerant boils and that sucks the heat out of the air passing through it. With all of its heat pulled out, the air is then cold and dry. Then the air gets blown through the vents and cools you off.
There are some other parts in the system, like the dryer (which dries the refrigerant) and the orifice valve which marks the point in the system between high and low pressure, as well as sensors and relays. But those three components are the most important.
Along with the refrigerant itself, that is. The most common refrigerants are R-12 (pre 1997 or so), R-134a, and R-1234yf (since around 2018).
Losing refrigerant is the most common reason an AC system will fail, but you need to do more than just recharge the system to fix it. The AC system should always be airtight, a leak is a failure point that will repeat itself. You can get kits that let you recharge your AC at home, but make sure to fix the leak first.
To help find and fix the leak, you can get a dye kit. Using UV dye and a special light, these kits highlight where the system is leaking so you can repair or replace the component.
Closed AC systems are hazardous to work on and releasing refrigerant can cause severe frostbite. So, AC system service and filling is best left to your NAPA AUTOPRO service specialist.