The Weaver Grip is the standard pistol or handgun grip used throughout the world's militaries and police forces. It allows rapid aiming of the firearm (and a large arc of fire) while maintaining a stable grip. This stable grip can be rapidly duplicated so that the natural point of aim remains the same through multiple shots and firing positions.
To assume the Weaver Grip for a rightie, one places the base of the pistol grip (where a magazine is loaded in an ACP or Automatic Combat Loading Pistol) into the left hand, such that the pistol rests in between the thumb and the forefingers, parallel to the seams in the palm. The grip should be centered in the seams that form a "V" shape in the palm. The right hand is then placed behind the grip of the weapon, in the same position that one would hold a glass of water. At this point, the operator brings the finger around the trigger group so that the trigger rests on the meat of the index finger. The right arm is extended and locked into place, and raised so that it is parallel to the ground. The left arm is held loose and relaxed, providing support to the right arm and weapon. The left elbow should be comfortable, but as close to directly below the right elbow as possible. Finally, cross the left thumb over the right thumb. If the weapon has a trigger guard, and the operator's natural point of aim and trigger pull tends to "pull" the rounds to the right, place the left hand index finger around and over the trigger guard.
Although the position is initially uncomfortable for most beginners, with proper coaching and practice in the correct form it becomes second nature.
U.S. Army Publication FM 3-23.35, Chapter 2 (Pistol Marksmanship Training) covers the different grips employed with the M9 Beretta 92F handgun, including pictures of the Weaver Grip. It can be accessed here.