I teach all of my students to play with their bottom lip slightly forward from the outset, rather than the clarinet style tighter embouchure with the lip folded right back over the teeth. I find that this encourages them to relax more as biting is less likely to occur, and also promotes a more full tone (not necessarily brighter, just more free and rich).
As a precursor to learning more precise embouchure adjustments in order to intonate, I ask them to put their hands around their neck just below the jawline and to sing an octave leap and feel what the muscles are doing in order to make the larynx adjust. This is usually enough to get them playing the first overtone from a low d without use of the octave key, thereby stressing the point that it’s our embouchure which does the work, and the octave key is simply there to provide a little help.
Having developed this control, I then talk a little about shaping the oral cavity, but only in broad terms (think ahhh in the lower register; ohhh in the middle and eeeee in the upper). As they develop more we use a drone to warm up and play a few long notes and overtones against, using the ear, rather than a tuner to adjust intonation. The important thing to make clear, is that the majority of the work happens away from the lips, at the back of the oral cavity and even the neck muscles.
I’m sure that others will disagree with me, but this method has served me well over many years of teaching.