Embouchure
In the typical embouchure, the mouthpiece is generally not taken more than halfway into the player's mouth. The lower lip is supported by the buccinator and chin muscles and rests on the lower teeth, making contact with the reed. The playing-position is stabilized with firm, light pressure from the upper teeth resting on the mouthpiece (sometimes padded with a thin strip of rubber known as a "bite-pad" or "mouthpiece-patch"). The upper lip closes to create an air-tight seal. The "double embouchure" in which the upper lip is curled over the upper teeth is not commonly used in modern times, however each player may eventually develop his/her own variation of the basic embouchure style in order to accommodate their own physical structure.
Three things are imperative to a full and quick-speaking sound: appropriate air pressure which is aided by diaphragm support, correct lip/reed contact allowing the reed to vibrate optimally, and perhaps most importantly a high tongue position within the mouth. This provides focus to the player's air stream and thus to his/her sound. The player's diaphragm acts as a bellow, supplying a constant stream of air through the instrument.
An approach, as taught by Joe Allard, conceptually is much simpler than most: natural. Allard taught that the your embouchure must conform to the mouthpiece and the mouthpiece is not round. Frequently citing anatomy, Allard depicted that when the skull comes down, the larynx and the throat are constricted, he had his students think of keeping their heads straight when they played. Allard also recommended that saxophonists use very little pressure from the top teeth and lip and just let everything rest naturally. Often quoting Douglas Stanly's "The Science of Voice," he said that keeping an open throat and a relaxed throat is contradictory. The summary of Allards approach to saxophone is keep everything as natural as possible, do not interfere with head position, tongue position, breathing, embouchure, just let everything be natural.
Read more about this topic: Saxophone Embouchure