There are many ways to breath. If you are a opera singer there is a right way to breath. If you are doing Pilates or yoga or Qi-gong there is a particular way of breathing that's building how exercise are constructed. Joseph Pilates himself has had breathing problem. He had asthma, thematic fever in his childhood and he adapted breathing called Lateral breathing from yoga which is breathing back and side of your rib cages as it is also recommended by Alexander technique teachers.
The intention of the breathing is also important. For example, If you want to relax and go to sleep you can breath through the nose and out through the nose to prepare yourself to sleep. If your intention to relax the body and prepare for exercise you can use Pilates breathing which we called as conscious breathing that Is breathing through the nose and out through the mouth while keeping abdominal engagement allowing side and back of your rib cage expand like an accordion while inhaling and exhaling allowing ribs and side of your ribs coming closer like having a tide corse around your diaphragm. Focusing on breathing will bring your life physical and psychological benefits.
To feel how to breath laterally , either lying your back in neutral position or sitting on your seat bones I would like you to to place your hands with your palms under chest. Your middle fingers are touching each other. When you are inhaling deeply allow fully expand your ribs laterally ( as in the picture accordion) notice your fingers gently apart from each other and exhale through the mouth slowly expelling all the breath from your lungs noticing your middle fingers meeting again ( as in the picture corse) repeat 10 times daily.
You can do this exercise at home in front of mirror monitoring if your shoulders moving unnecessarily when you are breathing laterally. As you regularly exercise correct breathing comes naturally. So be patient with yourself😊.