Every double acting air cylinder has these basic parts. A metal cylinder to hold everything together, a 'plunger' that the air pushes against, two connections to get the air in and out, and a rod connected to the plunger that goes in and out. That's it. Here's a simple animation to illustrate the motion...
As air is sent into the left connection (pressure is shown in yellow), it pushes against the plunger and the rod goes out. At the same time, air is released out of the right connection. To reverse the motion, air is sent into the right connection, pushing against the plunger on the other side and the rod is forced back in.
The trick to the double acting cylinder is that you have to let air OUT of the other side! This is an important feature of the double acting cylinder, and an advantage that gives you great control over the motion of the rod (but, more on that later!).
TIP: the most useful double acting cylinder I've found is one with 1/4" connections, 6"-8" stroke, 1" bore, and end clevis mounts. But that's just me - of course, most any cylinder can be adapted for haunt use!
Single Acting means the air cylinder rod is ONLY pushed in a single direction, either out or in. There is only one connection for air, and a little hole in the other end to let air in and out. A spring is used to push the rod in the opposite direction after air pressure is removed.
When selecting a cylinder for an application, remember that a double acting cylinder pushes in both directions, while a single acting cylinder only pushes in one direction.