As far as I know, the most important method of producing Ki is related to breathing.

I'm investigating the logical structure of Life itself(not the features of Life nor the gene) and the breathing begins with the logic of life. Usually speaking, breathing is a process of supply oxyzon to metabolism, I conclude breathing is a fundamental movement of life itself of interaction between inside and outside(circumstance).

A life exists with some body, which is consitituted with matters and is under the principle of entropy, thus its body need to supply energy to inside to keep its living state. The very mechanism is breathing. You can consider the ATP in every cell, which supply energy to each metabolic organ.

Producing Ki is producing vitality, but it is not producing breathing or increasing breathing. The best vitality consists not in the quantity of physical energy but in the harmony of the whole. The harmony of mind and body is important. The harmony of inside and outside of body is important, too.

We have to control the each part of the self. But how? Through the rhythme, I think.

Breathing penetrates every part of the body and even in the mind. For example, when we feel some particular passion we can find changes in the breathing. Thus we can control the rhythme of the life in the self by way of controling breathing.(See chapter 14 of PPT).

In TKD movements, every master emphasizes the importance of the breathing in each motion, the accordance of breathing and movements. After we've got skilled of the accordance, we have to exercise of controling the movement only with breathing. Then, only with the mind. For me, I'm not so much interested in only Ki, so I didn't exercised the next step. But I can suggested some guessed explanation, for the academical research.

Controling Ki may be considered as an special case of controling movement. When we have some anger at a man, we can feel the sudden flow of our bloody spirit without any movement. In this case, unless we oppressed our attack, we would attack in real. If we can accept this case, we can regard it as the movement of mind and Ki without action, and we can know it is possible to move Ki with mind.

In Korea, there are many high level trainers of Ki, so I can catch some informantion. They say, when concentrated only on Ki for health and spirit, the next step is to practice controling and accumulating Ki with your mind in your Dan jeon.

But they usually focus on the training the super power like telepathy. I think, it is more natural to train Ki with movements like that of TKD, and since it is natural it would be easier.

Another popular method of training Ki of China is Tai Chik Chuan, which also emphasizes the accordance of movement and breathing. The fundamental principle of TKD and Tai Chi Chuan is same, as far as I know : the accordance of breathing and movement under control of mind.

And you feel the flow of some kind of vitality whenever you move and you intend. It is the how to. Then, let me answer the last question.