I think the main thing to remember when breathing, is that when breathing in, the tum / gut below the ribs should expand and come out. This allows the diaphragm to move, giving space for the lungs to expand into. When breathing out, the tum should move in, pressing the air out.
In days gone by, people were told to expand the top of their chest, when taking a big deep breath in.
This is a waste of time, the lungs aren't in the top of the chest.
A useful breathing exercise, think it's used in yoga for relaxation. Breathe in for a count of 5, hold for a count of 5, and exhale for a count of 5. The count used can vary.