A surfboard fin or skeg is a hydrofoil mounted at the tail of a surfboard or similar board to improve directional stability and control through foot-steering. Fins can provide lateral lift opposed to the water and stabilize the board's trajectory, allowing the surfer to control direction by varying their side-to-side weight distribution. The introduction of fins in the 1930s revolutionized surfing and board design. Surfboard fins may be arrayed in various number and configuration, and many different shapes, sizes, and materials are and have been made and used.
Historically, surfboards had no fins; some amount of control was achieved through convex hulls and the surfer dragging a foot in the water. A common problem with these early boards was "sliding ass", in which the tail would slip sideways, usually causing a wipeout. The first fixed fin was introduced by surfing pioneer Tom Blake in 1935. In Waikiki, Blake attached a 12-inch (30 cm) long, 4-inch (10 cm) deep metal keel from an abandoned speedboat to his surfboard, and was immediately impressed with the results. Around 1936, Woody Brown independently added a fixed fin to his second surfboard design in San Diego, which further popularized the feature.
The stability and control fins allowed revolutionized the sport, though many surfers avoided them for several years; evidently they were thought dangerous. The feature grew more common in the mid-1940s and became the universal industry standard in the 1950s. Experimentation with fin design and configuration increased after 1966 with the popularization of shortboards. Parallel double fins, first introduced in the 1940s by Bob Simmons, became periodically popular. In 1981, Simon Anderson introduced the three-fin "Thruster" design, which has since become standard.
Both a skeg and "rail fins" stabilize the motion of the surfboard. They also contribute to the desired effect of converting the (kinetic energy) push of the sloped wave face combined with the rider's mass on the sloped wave face (potential energy) into redirected energy - lift (lift (physics)) - the surfer deflects his surfboard and fins off the water of the wave face (and/or vice-versa) to make forward progress across the wave face, or "down the line," that is, parallel to the wave crest and beach - riding parallel to the crest (perpendicular to the pull of gravity down the wave's slope) in this way is known as "trimming." Lift (aka "drive") from the board and its fin(s) is what enables all maneuvers in surfing.
Smaller surfboard fins mounted near the edge (or "rail") of the surfboard are known as "rail fins" and are seen in multi-fin arrangements (often in combination with a similarly-sized central fin further back on the board). Rail fins enable high-performance surfing, and are most often "single-foiled," with one flat side and one "foiled" side, as seen on an airfoil, for greater lift.
A fin configuration with fins near the edge of the board stabilizes and contributes lift during turning maneuvers, which contributes to the board's ability to "hold" during turning maneuvers. Rail fins are often seen in addition to a central fin, but can be used without a central fin as well. Some of the most popular multi-fin configurations use two rail fins (a "twin-fin"), two rail fins plus a similar-sized central fin mounted further back (e.g. a "Thruster"), or four fins (a "quad"). Rail fins are more or less engaged by the rider's heel and toes as they lean in the desired direction of their turn. As the rider does so, an "inside" rail fin sinks deeper and its angle of attack is increased, as is its lift-induced drag. Rail fins also add lift (known as "drive") in trim and with greater holding ability, enable steeper wave faces to be ridden and higher speed "down the line."
Rail fins are typically "toed-in," that is, the leading edge of the fins are oriented toward the centerline of the surfboard, which decreases the angle of attack in trim, which makes it easier to initiate turns. "Toeing in" rail fins also adds drag on the "outside" fin, as its angle of attack is negative during trim or in a turn. These combined factors of toed-in rail fins cause several issues: drag on a toed-in outside rail fin can slow the board down in trim, but it can also give a braking effect during turns that is useful. The inside rail fin (and the board itself) can be "pumped," attacked and re-attacked, by swerving up and down the face, causing acceleration down the line, or similarly pumped to achieve a desired trajectory through a multi-stage turn. At higher speeds, the drag off toed-in rail fins can cause surfboards to oscillate and become unstable - a phenomenon known as "speed wobbles".
Most surfboards intended for larger waves are longer (to increase hull speed for paddling, wave-catching, and surfing), and as most shapers orient the rail fins toward the nose of the board, a longer board inherently results in reduced toe-in of rail fins, therefore less negative angle of attack, less oscillation, greater stability, and higher speeds. Rail fins also typically have some degree of "cant," that is, are tilted out toward the rail they are adjacent to. This is a significant additional factor in lift at various attitudes, drag, and performance, as are the variables of other foils - including flexibility, thickness, and planform. Rail fins evolved into being and surged into popularity as riders (Simon Anderson, most famously) sought a solution to two major performance issues of a central "single" fin - both related to engagement of the foil: For one, a centrally-mounted fin is tilted up out of the water as the board is leaned over, and thus it loses more and more of its lift as the lean angle increases - if the lean angle is acute enough, the fin's tip can be the only area left in the water; the tip may then rapidly stall and, having lost its lift, become disengaged from the water, leaving the board's bottom as the only control surface still operating. Before rail fins became (extremely) popular, this tendency of "single fins" led to riders "nursing" turns - this tendency was a significant limiting factor on performance. The enhanced hold offered by rail fins during turning led to more types of maneuvers being possible. The other major issue leading to rail fins' use is the fact that a rider can use the lift near the rail to increase speed and performance on smaller waves due to the above effects and abilities of these foils. 
In Windsurfing, a derivative of traditional surfing, skegs are also often used as a central stabilizing fin (hydrofoil) located at the rear of the board. A windsurfer's skeg also has the effect of producing lift, which allows the rider to direct the craft laterally against the lift the sail (itself an airfoil) produces. The skeg has undergone numerous phases of development and, as with other foils, its design is determined by the balance of the pressures it experiences in use, including lift, drag (physics), ventilation and stall (flight).
Glass on fins are fins that are permanently connected to the surfboard through fiberglass. This type of fin was mainly used on older model surfboards. Glass on fins are broken easily and are hard to repair. You rarely see these types of fins today because a different type of fin has replaced them.
Removable Fin Systems The most common types of fins used today, removable fins are surfboard fins that can be unscrewed from the surfboard and be replaced by different fins or be moved about the board for a different setup in maneuverability and stability. In the early 90’s three Australian surfers invented the fin control system (FCS). Since its global release in 1994 FCS has become the industry standard; providing elite athletes and everyday surfers an abundance of fin designs and a platform to change the performance of their surfboard by changing fins. The system also streamlined the surfboard manufacturing process by making it easier to install fins into boards and repair damaged fins.
Flexible fins  fins are used on most rental boards because of liability. These fins are much safer than a hard fin because they cannot cut you. However it does lose some of the performance.
Tom Blake(One of surfing most influential fathers) invented the first fin used on a surfboard. Although Blake’s first fin was most like attaching a keel from a boat to the bottom of the board, Blake’s finding started the development of the fins in use today.
From Blake’s first fin, people, perhaps most famously Bob Simmons and George Greenough, have modified and invented new types of surfboard fins. Simmons was apparently the first to use more than one fin on a surfboard. Greenough made the fin flexible and took inspiration from the fins of fish(allegedly tuna) and dolphins. Bob Simmons used a twin-keel design on innovative wooden boards of his own design and manufacture in the 9'-10' range, which he rode in large surf at Windansea in California.
In the 1970s, multi-fin systems became much more widely used, in competition and by average surfers, as top professionals like Larry Bertlemann and Mark Richards enjoyed competitive success maneuvering shorter boards with twin fins in smaller surf and tighter radius turns.
It wasn’t till the 1980s that Simon Anderson invented the popular thruster set-up (three fins - two on the rail 10-12 inches from the tail end, one center fin 3-5 inches up from the tail) which stabilized the board compared to the twin-fin set-up, and provided more control and lifting surfaces in an effective configuration. The design was an immediate competitive success for Anderson, inasmuch as he immediately won 2 very famous surf contests using "thrusters," and the entire surfing world quickly followed his lead. The thruster is the dominant fin configuration to this day, in both recreational and competition surfing.
Surfboard Fin Setups and Shapes
The single fin setup is the original fin setup. Single fin setups are common on long boards. They are usually long and wider than other fins, which make the board controllable with only the one fin.
The twin fin setup has two smaller fins mounted near the rail. This setup provides extra speed and easier turning.
The most common setup, the "thruster" is a tri-fin. All the fins are the same size, with two semi-parallel (slightly toed-in, usually, and slightly canted outward, usually) fins mounted near the rails 10-12 inches forward of the tail and a middle fin at 3-5 inches.
The 2+1 denotes a larger center fin (for reference, larger than a thruster center fin) with 2 small to medium-small fins at a position close to thruster rail fin positions. The "sidebites" contribute some lift, control, and stability to the board when it is "on rail," arcing through turns. Typically, "sidebites" are removable, so the surfer can take them out for use in smaller waves, which gives less drag and freer turning. The 2+1 is a popular configuration for mid length to long boards.
The quad setup is four fins, two on each side, in a similar position to the rail fins on a thruster. The fronts are typically larger than the rears but this is not always the case. The rears are nearly always inboard and aft of the fronts . The exact measurements and configuration of the quad set-up can vary pretty widely. This setup is often used in short boards and provides more lift and control surface near the rail. There is no center fin.
The Twinzer is a design by Wil Jobson and similar to the Campbell brothers' "Bonzer," the fin set-up is held to be functionally integral and synergistic with the bottom contours of the board, specifically a "bat-tail" with an integral convex/double-channel. The fin set-up itself is four fins, two on each side, in a similar position to the rail fins on a thruster. The fronts are smaller than the rears, often roughly 1/3 the size, mounted ahead and outboard of the fronts, with ~8 degrees of outward cant, and notably, the fins' trailing edges are behind the leading edges of the main fins. The water coming off the trailing edge of the "canards" becomes part of the flow "behind" the main fins. This fact is held to enhance the lift and speed of the set-up, because of the "slot effect." The exact measurements and configuration of the twinzer are basically standardized by Jobson, but some variation is seen amongst different builders.
See Tunnel fin.
The Bonzer is a 3- or 5- array invented by the Campbell brothers in Oxnard, California in the early 1970s for the powerful waves of a well-known wave near their home. The Bonzer array is an approximately 7" center fin aft and either two or four delta-shaped fins ("runners") mounted near the rails in somewhat similar fashion to other rail fins, but they are substantially lower aspect and aggressively canted outward. The Bonzer array is firmly held to be an integral part of the Campbell brothers' overall board design featuring double concave bottom contours out the tail.
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- Dimpled Fins Technology | 3DFINS.COM