The structure of pneumatic schematics
In pneumatic circuit diagrams, the components are arranged the way that the flow of energy always flows from the bottom up (as opposed to electrical schematics). Thus the pressure source represents the first element, the actuator, the last element. In purely pneumatic circuits the processing of the input signals is also performed pneumatically.
Reading pneumatic schematics
Pneumatic circuit diagrams in practice usually consist of several circuits, that means you have a lots of valves and associated actuators (cylinders, motor). To read these schematics correctly according to their signal flow, proceed as shown in the animation below.
Remark: Concerning the diagram above: Press the button 1S1, the cylinder 1A moves forwards. Once it reaches its forward end position, the role switch 1S2 is activated. As highlighted in green, the roller switch 1S2 forms an additional condition for extracting the cylinder 2A in the circuit 2.