If you are reading this then you are most likely not a refrigeration technician. This website was created to help the Do-It-Yourselfer fix their own appliance and save money. That being the case, the explanation of How Refrigerators Work here will be as basic as possible.
When you take a cooler and fill it with ice and warm beer, immediately the ice starts to remove the heat from the beer, and the beer will remain cold, until the ice melts. This is because the ice in the cooler is at least 32 degrees. The heat from the beer cans is absorbed by the ice cubes, either by conduction, when the ice is in contact with the beer can, or by convection, where the heat is transferred to the ice cubes via the air.
If you had a manual defrost freezer, you could place an item directly on the evaporator coils, and the heat from that item would be transferred to the refrigerant by conduction. The warm air in a refrigerator is moved around by the evaporator fan, and as that warm air passes through the evaporator, the heat is removed quickly because the evaporator is extremely cold.
The exception to that rule is mostly high end refrigerators, that have multiple sealed systems. When the system is operating, the temperature of the evaporator is extremely cold, as low as -35 degrees for example. As the air passes through the evaporator, the heat is immediately pulled out of the air. The moisture that was in the air has a rapid change of physical state from a gas to a solid.