How do air brakes get there compressed air?

There's an air compressor mounted to the engine. That compressor charges one (or several) tanks. Air from the primary system is fed continuously to the emergency chamber of the spring brake chambers

• this provides hold off pressure to release the spring brakes.

When the treadle valve (brake pedal valve) is depressed, air from the primary air system (and usually the secondary air system for the front axle) is routed to the service chamber of the brake chambers, and this usually rotates and S cam to push the brake shoes out into the brake drum (although specifics at this point will differ with disc brakes and piston brakes).