First, start by taking a slow, deep breath. By inhaling and exhaling slowly, students can learn the feeling of inhaling deeply and fully.
For example, it's better to practice with a metronome, such as inhaling for four beats and exhaling for four beats, or inhaling for eight beats and exhaling for eight beats, for a quarter note of 120. I think one to two minutes is enough.
Everyone breathes all the time, so breathing techniques for instruments are not something special.
It's a very natural thing, so once students can play an instrument, it's better to combine it with other practice, such as taking four beats of inhalation before a long tone, rather than taking a long time just to breathe.
Embouchure (shape of the mouth) is an important issue for any wind instrument. If students look at photos or videos of skilled players playing each instrument, they can see the unique embouchure characteristics of each instrument. However, since mouths and teeth alignment vary from person to person, just check a few points.
What is common to all instruments is not to put air inside the lower lip or pull the lips to the side.
For brass instruments, it is especially important to create a good embouchure because the sound is produced by the vibration of the lips. The impression of making a sound for the first time in a life is particularly strong, so even if the embouchure at that time is unnatural, the student will remember it as "the way I play".
Before making a sound on a brass instrument, it is better to
buzz with their lips only, place the mouthpiece there, and get used to the feeling before putting on the instrument.
I once heard a story about a trumpet student at an elementary school who had been making sounds by vibrating her "upper lip" and "tongue" for a long time, and no one had noticed until the student started practicing tonguing. When I tried it, I was able to make a sound that way. If instructors just hand students a mouthpiece and say "try making a sound" without any explanation, students may end up taking a terrible detour like this, so be sure to teach them the very beginning very carefully.