There are a lot of troubleshooting pages on this website to help you get your air conditioner up and running again, but understanding how an air conditioner works is a good first step. If you understand what all the parts are, and what they, it will help you in figuring out the problem.
Your air conditioner is comprised of three main sections, all of which have to be working for your home to get cool. They are: the furnace (or blower unit,) and the indoor cooling unit (the evaporator,) and the outdoor unit (called the condenser.)
Below is a brief description of these three sections and what their jobs are. Understanding what they’re supposed to do will help you determine which part of your system is not working. Once you have an idea as to which section is malfunctioning, you can then go into more depth by clicking the appropriate links below.
The Blower Unit or Furnace
Your blower unit is the first thing you hear kick on when you turn on your AC. It draws your home’s hot air and moisture in and across your evaporator coils. The evaporator coils cool the air and the blower fan disburses the cool air throughout your home.
The evaporator is filled with a refrigerated gas called Freon. The freon, the evaporator and the compressor all work together to convert this freon from a gas into a liquid, and from a liquid into a gas. Most people get confuse when learning about this for the first time. So, to keep it simple, the important thing here is that the evaporator is where the coolant evaporates.
Coolant that is evaporating is cold.
Also important to note is that this process creates condensation. The condensation is removed from your home through a condensate drain line. If this line gets plugged, it can trip a safety switch that will shut the unit down (to prevent water damage.)
The cold air created by the evaporator gets blown into the home, and the heat created by the process leaves the home through the condenser coils.
The process of evaporation causes heat, and that heat must leave your home, it does this via the condenser coils. The giant gray box outside your home is the condenser. That big fan blows a way the heat created by the evaporator coils, and the cycle continues.
Above was a simple overview of the process. Below are a few more key components if your a nerd like me and would like to go even more in depth.
Before we assigned the home air conditioner three main parts. When you dig deeper, you realize that there is a fourth component we refer to as the metering device. Below is Wikipedia’s more in depth explanation of the system that includes the metering device.
A basic refrigeration cycle consists of four major elements, a compressor, a condenser, a metering device and an evaporator. As a refrigerant passes through a circuit containing these four elements, air conditioning occurs. The cycle starts when refrigerant enters the compressor in a low-pressure, moderate-temperature, gaseous form. The refrigerant is compressed by the compressor to a high-pressure and high-temperature gaseous state. The high-pressure and high-temperature gas then enters the condenser. The condenser converts the high-pressure and high-temperature gas to a high-pressure liquid by transferring heat to a lower temperature medium, usually ambient air.
The high pressure liquid then enters the expansion valve where the TX valve allows a portion of the refrigerant to enter the evaporator. In order for the higher temperature fluid to cool, the flow must be limited into the evaporator to keep the pressure low and allow expansion back into the gas phase. The TXV has sensing bulbs connected to the suction line of the refrigerant piping. The gas pressure in the sensing bulbs provides the open force to open the TXV, therefore adjusting the flow of refrigerant and the superheat. 
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