When I learned how to play Chinese flute (笛子) in high school, I had to do full lung breathing. Chinese flute is a loud instrument. The sound it created is being maximized by a reed membrane. It usually plays the theme in group ensemble, which part is played by violin in Western instrumental music. I was so amazed by my sifu's ability to increase his lung capacity when he played his instrument. "Takes time to increase your lung capacity" that is what he said. Somehow I got it after a year into training.
The benefit about playing the flute for increasing lung capacity is that there is always a feedback. Lacking in powerful air outflow, the reed membrane cannot be fully vibrated, and that can be readily noticed! And without the required length of breathe, the tune will have to pause in the wrong places The negative part is flute teachers do not know how to teach you how to do full lung breathing "Takes time to increase your lung capacity". Your only advice.
In doing chi kung, the case is just the opposite. You do not have the necessary feedback but, given a good teacher, there are ways to train you to do full lung breathing. Below is the way I use in my coaching. Please use it only as a reference, you will need the personal attention of an experienced teacher to do it properly, which essentially means your teacher needs to judge whether your are using the correct muscles and be able to correct you on the spot.
Your lungs are caged in your body in the bottom by your diaphragm, at the top by the muscles around your neck and shoulders, and at the sides by your rib cage. Full lung breathing means expanding your lungs maximally downward, upwards and sideway. During the whole process, your hands are to be in "zhan zhuang stretch" (that's way zhan zhuang is so important) and the power of the stretch has to be synchronized with the contraction of your breathing muscles. In other words, you have first to learn zhan zhuang before attempting to do full lung breathing in chi kung.
The next thing you should note is that you should image your lungs in the form of a cauldron, or housed inside a cauldron. Cauldron visualization is of paramount importance in Taoist meditation (Neidan). A good practice of Taoist meditation presupposes the ability to do full lung breathing. The mental focus during full lung breathing is on the outside (the shell) of the cauldron. A success criterion is the internal sensation of feeling your cauldron expanding and contracting sluggishly.
The mechanism is not complicated. The steps are important. The first step is a deep breathing focusing on expanding your cauldron upwards and downwards only. Expanding means breathing in, contracting means breathing out. Expanding downwards is what people call abdominal breathing, but that is NOT enough, slight expanding upwards is also required. Expanding upwards is difficult because it can easily make you raise your shoulders and your breathing will be out of good control. To counteract this tendency, your head shall bend down synchronically. And your sternum shall be relaxed (in tai chi lingo: 函胸), you will also feel chi running up your back during breath-in (in tai chi lingo：拔背).
After you have done the up/down breathing to its maximum, hold your breathe for just a second and you do the second left/right expansion of your rib-cage. The key is to straighten your head to facilitate the breathing. This is what people called chest breathing, in which the sternum raises as well.
Many tai chi sifu do not teach (or do not know how to teach) full lung breathing. Many meditation teachers do not teach (or do not know how to teach) full lung breathing. "Take time you will have it", a possible response. As I explained above, unfortunately there is no good feedback system in tai chi and meditation like when learning how to play a Chinese flute.