Since many students will not have instruments or won’t be willing to practice on a daily basis, practice while doing more desirable activities. To teach embouchure without an instrument starts out the student with good habits before they begin playing the instrument. Once they learn how to form good embouchure without the mouthpiece, when they get their instrument, much of the work is already done.
Before getting out the saxophone you can you your thumb to model a saxophone mouthpiece. Insert your thumb into your mouth. Only put it about up to your nail and no more. The thumb should be straight into the mouth with a slight downward angle. This is the same angle the clarinet should be held. The corners should be in (this is to prevent air leaks) and the teeth should rest on top of the thumb. Keep the lower jaw loose and only apply enough pressure to prevent air leaks. The embouchure can be thought of as a rubber band around the mouthpiece.
When using a real saxophone, nothing should change. This will give you an opportunity to check if there is an air leak in the embouchure. The amount of mouthpiece that is inserted into the mouth is the same as one thumbnail amount. Too much mouthpiece will cause a honky sound. Another way to think about it is to make an O shape with your mouth. Smiling produces a bad embouchure by having air leaks and pressure in the wrong areas of the mouthpiece.