The key components of your central air conditioning system are:
The outdoor condenser unit is the big box outside your house which contains the compressor, condenser coil, and the condenser fan, which looks like a propeller.
The furnace is usually down in the basement. It draws warm air from upstairs and blows it across the evaporator which removes heat and distributes the cool air throughout your home.
The evaporator is a coil/heat exchanger/radiator looking thing that sits adjacent to your furnace. For the majority of gas or oil upflow furnaces, it will sit above the furnace in the supply. For electric furnaces, it often will sit in the return duct.
The evaporator will be hidden in the ductwork but will always have a copper line going in, a larger foam insulation covered copper line going in, and a drain pipe for condensation going to a pump or into a floor drain.