• How do you play the trumpet? Sound is produced on the trumpet when the player sends energized air into the trumpet with the intention of making a sound.  The blown air vibrates the air already inside the trumpet (concept borrowed from John Harbaugh, https://www.youtube.com/watch?v=MVs2G60-ilo&t=466s).  The lips sympathetically vibrate with this standing wave in the trumpet, creating a tone.  The lips will naturally come together when air is blown through the trumpet (Bernoulli effect). 
• Therefore, the air and the ear plays the trumpet. You do not need to buzz your lips.  In fact, doing so will cause problems.  I discourage lip and mouthpiece buzzing for this reason.
• Breathe as naturally as possible. Lay down and observe how you breathe in this position.  The abdomen should rise on the inbreath and fall on the outbreath.  When standing, the gut should relax on the inbreath, and the chest should rise and expand on the outbreath.  Then, let the music teach the body how to breathe.
• You do not need to use a lot of air to play the trumpet. Too much air will cause problems.  You need just enough to touch and vibrate the air already in the trumpet.  This is very little.  You do however need air that moves. 
• Cut a normal drinking straw to about 6 inches in length. Practice blowing through the straw in short bursts (lips about ½ inch from straw) and making a pitch/tone.  This is the proper way to produce a sound on the trumpet.  It can also be helpful to practice blowing air through the trumpet in short bursts (no mouthpiece, lips about 1-2 inches away from lead pipe) and see if you can vibrate/resonate the pipe or bell.  This should sound like a timpani strike or a “thud”.  Blow air straight through the trumpet.  Let the air move freely.  You should not feel the air moving back towards you.  If you do, you may be using too much air, or the lips might be getting in the way.  Transfer this feeling and sound of resonating the pipe or bell to trumpet playing (exercise could be misunderstood in writing, better to demonstrate in person; exercise borrowed from MWNA program designed to retrain brass players:  https://musicianswellness.com/).
• The teacher should encourage the student to focus on feeling the air travel freely through the pipe and hearing how they want to sound. This external focus of attention will be a far more successful method of motor skill development than teaching the specific motor skills themselves (based on research by Gabriele Wulf, http://gwulf.faculty.unlv.edu/).
• The teacher can however correct bad physical habits that present in their students. Otherwise, teach by having the student envision the sound they want.  While demonstrating is helpful, description, recordings, and the student’s imagination are just as helpful.      
• Many trumpet playing struggles can be addressed focusing on the above concepts.

Concepts borrowed from MWNA program designed to retrain brass players:  https://musicianswellness.com/.