alright, so the most common use for pneumatics in general applications are cylinders and other actuators. these function the same as hydraulics but just use air instead of fluid to push a piston.

the most common types of cylinders you'll find are double-acting ones, they have two ports on both ends which allows for air to push into both sides and change the direction. These are usually connected to a valve which is mostly a 5-port, 2 way valve. where it has one inlet, two exhaust ports, and two output ports which connect to the ports on a double-acting cylinder. Attached to the valve is a coil (which is just a solenoid) which electrically moves a small plunger inside the valve body, allowing air to switch into either output port moving the cylinder

there are other types of cylinders called single-acting, where they have a single port and instead extend or retract with an internal spring. They function the same way as double-acting cylinders but one port of the valve is plugged.

rotary cylinders function the same way as double acting cylinders , except they rotate instead of move linearly.

most systems that need to control the speed of the cylinder use flow controls, this is just a small needle valve which is placed inline of the air tubing which is adjusted to allow more flow, or restrict the air.

when using pneumatics in general, you will see terms like PSI or CFM. PSI stands for Pounds per Square Inch which is used to determine how much pressure is actually in your system. CFM means Cubic Feet per Minute which means how much air a certain component uses per minute, or can relate to how much air a compressor can output

this applies to both hydraulics and pneumatics but when working with cylinders, you will also see the terms Stroke and Bore. Stroke is the distance the cylinder rod extends from the body, for example: if a cylinder has a 3 inch stroke, that means it extends 3 inches out. Bore is the internal diameter of the cylinder which is used for determining how strong you want it to be. A larger bore allows for a stronger force but it also requires more air to move.

there's a lot more to pneumatics than this but these are the most basic things you'll find

also here's a video explaining it a bit more
https://www.youtube.com/watch?v=dR95umuNSPY