I don't see any guide or any real description of the benefit of training your diaphragm (other than taking deep breaths by pushing your stomach out. But how much? How often?)
Don't push your stomach out. Let the stomach be pushed out when you breathe in. There's a difference.
The simplest way (I think) to find a 'deep'/connected breath, is to breathe slowly all the way out, making a 's' sound, until there is no more air left. Then, hold for about 4 seconds. Now just relax and let the body breathe in on its own.
At some point you learn to separate action and observation: you can focus your attention on the breath, meaning the sensations associated with breathing (air flowing through your nostrils and over your upper lip, belly slowly moving), and still let your body control the breathing action automatically.
In The Mind Illuminated, there is a comparison of this to catching a ball: instead of seeing the ball and trying to directly control your arm to catch it, you focus on your intention ("Catch the ball") and let your body simply act on (implement) this intention.
The great thing is that while you practice this separation of action and observation using the breath, it will apply generally to your life. Very powerful for managing your emotions: instead of being your emotion when you become aware of it, and identifying with the urge to act on it, you learn to observe the emotion without that observation having direct effects on your actions. You can choose to act on it, or choose not to.
Diaphragm breathing is also part of the training for classical flute players to breathe. It is how babies breathe naturally.