I did a very brief summary of Landing Signal Officer (LSO) history and responsibility here:
http://thanlont.blogspot.com/2009/05/waving-them-aboard.html This is an expanded discussion that is limited to landings on axial-deck carriers.
The LSO was a very early innovation in the development of aircraft carrier operations. He stood on a platform on the aft port side of the ship and visually coached the pilot of the approaching airplane into position for a successful landing or directed him to go around for another try.
According to legend, the first LSO was CDR Ken Whiting, the executive officer of Langley, the U.S. Navy's first aircraft carrier. He reportedly watched many of the first landings from what would become the LSO position and eventually grabbed two white sailor's hats to make his corrections more visible. Standardized signals and the creation of the LSO's paddles followed in short order.
To land on an axial deck carrier, the U.S. Navy pilots approached as for a short field landing, "dragging" the airplane in a speed just above stall and a constant altitude only about 20 to 30 feet (wheel height) above the deck. Upon receiving the "cut" signal from the LSO, the pilot closed the throttle, which resulted in an immediate descent onto the deck in the midst of the landing wires.
The pilot first had to get to the start of the "groove", which was where the LSO's coaching began. At the risk of oversimplifying, the groove began a few hundred yards (less for propeller-driven airplanes) behind the ship, where the pilot had completed his turn from his base leg and was lined up and on speed at approach altitude in level flight. At this point, the LSO's signals were visible and he began coaching the pilot as to height, airspeed, and line up in that order of priority. Those signals were advisory in nature relative to the two mandatory ones, which were the cut and the waveoff. Given the speed of the aircraft, there was only a few seconds for coaching and correcting before the LSO had to give the pilot either the cut or the waveoff signal. These were the basic signals:
There were several more, as illustrated in this article from Naval Aviation News in 1945:
Note that these were the "Day" signals. I haven't yet found a description of the corresponding "Night" signals.
The "slant" or "tighten turn" were used to coach the pilot as to line up, since—particularly with the F4U Corsair—the groove might well begin while the pilot was still turning to line up with the carrier. If the LSO thought that the pilot was in the process of making a good approach, he might therefore be given a Roger signal even while in the turn.
A wave off wasn't necessarily indicative of a poor approach. In order to bring all the airplanes in as quickly as possible, the interval between them left little margin for a problem getting one out of the landing area. A wave off might therefore result from a foul deck.
The LSO might also realize that the deck movement, which he could feel before the pilot could see it, was out of sync with the airplane's ability to settle into the landing area without being long (deck descending) or touching down too hard (deck rising).
There were also variations in the LSO signals, possibly unofficial and specific to an Air Group. For example, these are the ones that Frank Bon used to wave AD Skyraiders in 1955:
Note the addition of the angling approach signal, which meant that the pilot was coming in at an angle to the axial deck rather than turning to line up with it. That may be the signal that this LSO is giving the pilot of the F9F Cougar during field landing practice or he may have stopped waving and commenced to relocate himself farther stage right. (The caption given with one instance of this picture's publication that he's giving a cut signal, which is clearly not the case.)
This is a good illustration of the cut signal:
Note that jets had to be cut farther out than the propeller-driven airplanes because they did not lose speed and settle as quickly:
The student LSO, who was invariably a Naval aviator, had to become well acquainted with what a good approach looked like, both in altitude and speed, from the LSO's viewpoint. With jets, angle of attack was the better indicator of the proper approach speed since the speed varied with weight (which could be significantly different due to the jet's much higher fuel burn) and the angle of attack did not. Early on, jets were marked with stripes, first on the nose and then on the vertical fin, to provide an angle of attack reference based on which stripe a certain part of the airplane, like the horizontal tail, was aligned with.
Getting the picture mean watching many landings waved by an experienced LSO. (The Brits also had the trainee LSO practice with experienced pilots who were unlikely to be misled by LSO judgment errors.) At first, the neophyte LSO would only be qualified to work with one type of aircraft. Over time, he might gain enough experience to bring other types aboard.
The paddles used were traditionally hand-made by the LSO himself. As a result, there was significant variation, for example round vs. square or oval.
The LSO initially wore the usual working uniform.
Whatever that might be.
When the higher speed of jets required that the LSO be visible from a greater distance, standard flight suits were modified to provided a more obvious indication of the relationship of the LSO's body and his arms.
The requirement for all-weather and night landings increased the need for better visibility of the LSO. This was initially provided by a suit with stripes and paddles that fluoresced with black light but that was soon replaced with a lighted suit and paddles as shown here.
A readily available example of the activity on the LSO platform is provided by the excellent movie,
Bridges at Toko-Ri.