Residential central air conditioning systems that need to cool and dehumidify uses a condenser, evaporator coil, and refrigerant piping to operate. The means of moving the air might differ (furnace, air handler, etc.), but the principal is the same for all split systems. Freon is compressed and run through a series of tubes to remove as much heat as possible, then piped to an evaporator coil as a warm liquid. Expansion of the compressed liquid causes it to cool, and as the air passes over the coil, heat is extracted. The cool liquid becomes a cool gas as it gathers heat from the air, and is drawn back to the compressor to start the procedure again. As the air passes over the evaporator coil and cools, moisture in the air condenses and drains off as condensate.
Some hybrid and geothermal systems use cold water instead of freon until the temperature gets to a certain point, but the majority of systems use freon for the entire cooling cycle. In arid climates when dehumidification is not needed, only cooling, evaporative air conditioning is practical and economical.
Evaporative systems can be as simple as a pond of water on a flat roof, or more involved with the use of air handling equipment and special fabrics. By running water down loose material that is suspended and blowing air through the wet fabric, the evaporation of water will lower the air temperature and raise the humidity. The water that does not evaporate will be cooled down enough to contain in a vessel and become a secondary source of cooling by moving air over the vessel to create air conditioning. Split systems that use freon are of the same design, no matter what the source of air handling equipment used(furnace, heat pump, hydro-air, etc.).
Basic troubleshooting for split systems: First make sure that the thermostat is set lower than the actual room temperature. The selector switch must be on "cool". If the thermostat is programmable, be certain it has fresh batteries. Check for power by moving the fan switch from "auto" to "on". If the blower runs, there is power. If nothing happens, a control is burned out or power is disconnected. If the system uses a furnace for heat, check that the emergency switch is on. If you are familiar with the fuse or circuit breaker panel, check for blown fuses or tripped breakers. Correct the problem one time only. If it repeats, call for service.
With the selector switch on cool and the fan switch on auto, move the thermostat well below room temp. If the blower runs but the condenser(outdoor unit) does not, check the circuit breaker panel. If the breaker is on, examine the condenser. Some have a high pressure cut out. It is a button sticking out of the cabinet, usually near the refrigerant lines. Push it in as far as it will go to reset it.
If both units are running and no cooling is taking place, touch the larger of the two copper lines exiting the condenser. If it if warm, the system is out of freon or the compressor is down. If the line is frozen or iced over, the is an air flow problem inside, such as clogged filter or too many registers closed or an object covering the return duct. A low freon charge will also cause a freeze-up. Shut the system down and let it thaw out completely. If it freezes up again, call for service.
If the unit is in the basement and has a condensate pump, the control wire for the condenser might be wired through a safety switch on the pump. Check to see if the pump is plugged in and operable. If the unit is in the attic, there could be a float switch in the air handler or in the safety pan that will shut the condenser off if the drain is clogged. Water around the unit is evidence of trouble. Call for service.