The chin should be firm (not bunching up). The corners of the mouth should spread to a point but NOT too far. As you go higher, the lip opening (aperture) should become smaller and not stretched. As the chin muscles pull down it keeps the lip from stretching outwards too much. (In Philip Farkas’ picture of 40 top professional players’ embouchures, they All played with the firm chin and corners not stretched too much in what we call a smiling embouchure). The smiling embouchure will make your tone not as good/thinner sounding, not as good of control, not as good of endurance and usually sharp pitch in the upper register.
We don’t want to get too “puckered” of an embouchure either. We would call it a “whistling embouchure.” With a correct embouchure, it’s like we start to smile but stretch the skin across our chin.
Also do not want puffed cheeks; it’s an indication that areas of the embouchure are too loose.
Another thing we do not want to do is have the lower lip tucked under the upper lip too far to go higher. A small bit of the lower lip coming under the lower lip is fine, but the primary means the pitch going higher should be by the aperture (lip opening) becoming smaller. Having the lower lip sliding far under does not work well in the long range. If you are getting this it easily in your best interest to change. Usually if this is happening, the chin will also creep up in the high register. One of the most helpful things to fix it is to pulling chin further down (and that’s the main fix for the “smiling embouchure” as well).
Sometimes a good way to help get a proper embouchure is to buzz WITHOUT the mouthpiece. It’s difficult to get a “smiling” or “whistling” embouchure that way. However, when you get onto the horn, you DO have to shift your tongue position down, or it comes out “nasal” sounding, pinched. Even though that can happen, it’s worth the help in getting a correct embouchure formation. When I’ve had students initially test out the horn as a possible instrument, I’ve had them buzz without the mouthpiece from the very beginning and occasionally go back to it. Since I started doing that, I’ve had more students getting correct embouchures from the very start.