A three-stage process
Calmness is key: Relaxed breathing engages the vital process of diffusion, which is the process of gas exchange that takes place within the alveoli. It is this that causes the critical two-way transfer of oxygen and carbon dioxide, essential to the blood.
Also called 'thoracic expansion': Deep breathing includes holding the breath for a second or two (where possible) to encourage diffusion. After deep breathing, a few more relaxed breaths are recommended before continuing to the third 'huff' stage.
The critical stage: The huff is the point when the sputum is released, however if release is only partially successful, simply relax and repeat the three steps.. it is a process and not a test!