Breathing has long been used as a technique to reduce anxiety. In fact, Simply Amazing Training recommends a popular and effective technique to try just before a public speaking event. This technique, box breathing, is also found in yoga.
One component of yoga is Pranayama. Simply put, this refers to breathwork. Breathwork is a collection of breathing techniques that can help to reduce stress and anxiety, and even depressive states. The techniques work to keep us in a rest and digest state. Therefore, they are great to help us calm the mind and body before (and during) a public speaking event.
When we are in fight-or-flight, our breath becomes shallow and rapid. By consciously working on slowing down and deepening the breath, we can signal to the brain that we are, in fact, safe.
This triggers a response in the brain to slowly restore normal function in our bodies, meaning your heart rate will return to normal, and your muscles will stop shaking.
Though this might not happen immediately, with consistent practice you will start to notice some subtle shifts.
There are several beginner-friendly techniques that focus on deep breathing and encourage slow breaths. I have linked videos to my favorite two practices below. I recommend starting with Belly Breath, as this helps to develop breath awareness. When you are comfortable with that, move on to 3-Part Breath, as that requires a little more focus.
You can also read more about Belly Breath and 3-Part Breath to get a closer look at how they benefit the mind and body.