How do pump diaphragm carburetors work?

The diaphragm carburetor is found on many small engines. These engines power everything ranging from lawn equipment, generators, and even RC aircraft.

Unlike a conventional "float" style carburetor the diaphragm carburetor will operate regardless of its orientation, even upside down!

The internal workings of a diaphragm carburetor are simple in design, but complicated in explanation and consequently lengthy to discuss.