Whether in public speaking, swimming, running, singing or sleeping - breathing is the fundamental thing that we do, so our resistance to improving it is problematic.
A friend recently told me that his partner could spot when we was upset by him holding his breath. Saying 'breathe' to someone who is irritated probably has the same effect as saying 'Relax' to someone who is angry. Our breath is however a very good gauge of where our mind is at. Although it is automatic, it is one of the first things to go when things start to unravel.
One very simple technique Yoga teaches is 'abdominal breathing'. This is relearning the basic way we breath to use the full lungs. Often when we try take a deep breath, it is short, forceful and in our chests. In yogic breathing you learn to start by using the abdominal muscles. As you breath in slowly, the abdomen raises first. As you can see in the picture below, this makes space for the lungs to expand. By contracting the diaphragm, the belly rises. This is the opposite of what becomes the way to take a 'deep' breath where people end up sucking their tummy in. That is why it needs practise. A useful technique to learn to use your diaphragm is to lie on your back and interlock your fingers loosely. As you breath in, your fingers should part slightly. As you exhale, they come back together.
I am all for practical steps towards happiness. A great first step is breathing properly.