First, you should know that marshalling signals -- those gestures and upper body positions meant to guide or lead one or more individuals in some effective way -- are not unique to aviation; some of those shown here may have other meanings. Second, even within aviation, you may not always see it done exactly the same way; some standard signals suggested by, for example, the Air Transport Association of America might be improvised a bit and slightly modified. (Someone more limber might make it seem a bit like break dancing; someone else might be feeling a bit stiff that day, etc. Don't expect military standards everywhere you go; just try and get the gist of it all.)
Here are a few safety considerations. First, whenever you're taxiing near anyone, never rush things; take it slow. The more confined your maneuvering space becomes, the slower you should go. Once you've got that propeller stopped, make it known that you have taken the key out of the ignition and you've turned off the master switch. (I always make a bit of an exaggerated arm motion to the line person that tells him or her that the key is on top of the dashboard, and not in the ignition.)
In places where it's busy and your aircraft might need to be moved, understand that it might be best and actually safest to leave the parking brake off. Finally, when you park somewhere without benefit of specific directions, be wary of just where that is. You wouldn't want to find out later that you had parked behind a jet and you'd never put on the gust lock.
Normally the flagman will stand in front of the airplane and to its left side so as to be conspicuous in the pilot's field of view. But obstacles, footing, or just a lack of enthusiasm could lead the marshaller to stand elsewhere relative to the pilot's seat. (A really savvy line person will stand to the right front corner of a helicopter, recognizing that the pilot normally sits on the right side of that breed of flying machine.)
These signals are by no means exhaustive; there are still more. Also, you may see the use of "Day-Glo" paddles or, at night, illuminated wands -- like those shown in the accompanying photos -- rather than just hands and arms. These are described from the pilot's vantage point, since the two players always face each other and the potential for confusing left and right always exists. To remove all ambiguity, when a description involves the signaler's arm motion or position, I'll state specifically just which arm that is: left or right.
There are some other signals that you're not likely to see at general aviation airports. The "push-back" signal, frequently seen by airline pilots, is kind of like a gentle "shoo" as the arms are raised upward from the sides. The "next flagman" signal consists of both arms pointed upward, moved outward to the sides, and then pointed in the direction of the next taxi area or signalman (another version uses one arm down and the other simply moved across the body and extended in the desired direction). It's hard to know how to comply with the "insert chocks" signal while behind the yoke of an airplane.
A complete depiction of hand signals can be found in the Aeronautical Information Manual.
Some of these signals, one might argue, do seem a bit archaic, stilted, or perhaps even counterintuitive. But becoming fluent in this aviation version of sign language is in everyone's best interest. We owe it to those who are laboring on the front lines at our airports, some of whom are young people working their way into an aviation career the hard way (and whose presence provides businesses with safety and satisfied customers). The least we should do is give them a chance to get that experience without too much undue concern that we're going to harm them.
And we owe it to ourselves to operate our aircraft as safely as possible on the ground when in close proximity to other aircraft, equipment, and people -- as well as in the air.
Jeff Pardo is an aviation writer in Maryland with a commercial pilot certificate for airplanes, and instrument, helicopter, and glider ratings. He has logged about 1,200 hours since 1992. An Angel Flight mission pilot, Pardo has also flown for the Civil Air Patrol.