When I first learned to shoot a handgun, my mentor was a former WWII rifle, pistol, and hand to hand combat instructor for the US Army Rangers who were among the most elite troops who fought during WWII. My mentor worked with Col. Rex Applegate (who taught the methods of Fairbairn and Sykes) to develop marksmanship training programs which included the kind of point shooting developed and advocated by Fairbairn.
The method worked well and was easy to learn. The shooter is required to be able to shoot while gripping the pistol with both hands simultaneously and with either hand individually. The method includes firing with one hand held at waist level at distances out to 10 feet and with both hands with arms extended just below chin level out to distances of 10 yards or a little more. Although the method has been frequently described by Ayoob and others as a "body indexing" style of shooting, it does not rely exclusively on body indexing when shooting at distances under 10 yards. At close range, it seems a lot like modern point shooting from an isosceles position.
My mentor demonstrated with deadly effect during WWII that the method worked effectively in combat. Even though I first learned the method as a 10 year old about 55 yr ago; with a little annual refresher and warm up practice, it still works well for me today.
Contrary to what many are saying on this thread, learning point shooting by the Fairbairn and Applegate method did not require a large amount of practice nor require the expenditure of a much larger volume of ammunition than was required by training in conventional marksmanship techniques which relied on the use of sights. In the Rangers, soldiers were always taught both point shooting and aiming with sights. Neither Fairbairn nor Applegate ever advocated using one system to the exclusion of the other. However, they both were known to have stated that in combat, it is likely that point shooting (with a handgun) would be useful more often than techniques involving the deliberate use of the sights. But Fairbairn, Applegate, and my mentor stressed the use of the sights whenever you have time and at ranges greater than 10 to 12 yards.
Fairbairn and Applegate realized that under combat conditions a soldier will often miss regardless of the shooting technique used. So they taught their recruits to shoot more than once with a pistol whenever possible.
Although there have been improvements in technique and instruction during the last 60 years, the original methods taught by Faibairn and Applegate still work effectively and are easy to learn.