This is to really clear some air around. Alot of teachers place much emphasis on diaphram training, and yet even more singers see a powerful diaphram as the pinnacle of vocal skill.
You don't need to learn to use your diaphram. In fact, forget about it when you sing.
Every normal person uses his/her diaphram to breathe in and out. It is a normal body function. This process get messed up when a person 'try' to use the diaphram artifically during singing, or the body tense up so much that nothing is 'normal' anymore.
This is of course not saying that singing is totally unrelated to the diaphram. As a student, you'll still need to understand the function of it in various singing modes, e.g. sustian, cresendo etc. After knowing this, and totally comfortable with how it feels like, one should not be concern with diaphram breathing during the act of singing. Knowledge, in this case, grants you freedom of movement, not the power to control.
In teaching, their are various ways to introduce the functions of the diaphram to students. It is impossible to describle those drills here, and it is highly possible that someone can follow those instructions and do otherwise. It's quite an abstract feeling, cause' the muscle is hidden in the middle of your body, not quite the 'pump' feeling you'll get when you flex your biceps.
The most empirical way is to do some research readings, either dedicated singing books(try Esplanade Library) or just your normal Biology Textbook. All my former vocal instructors brushes through this topic, and I really understand the diaphram through reading myself.
If someone tells you do 'diaphram exercises' to strengthen your diaphram so you can sing better, then ask them; does a piano student have to do finger strengthening exercises to improve his playing?
One little test; until this very moment, while you were reading my post, you are breathing naturally with your diaphram. Your stomach is going up and down right? Of course right now I mentioned it, you tense up and notice yourself, and start to hold your breath into your chest.
In this little experiment, you are unable to differentiate between diaphram breathing and chest breathing. As a result, no matter how hard you try, you always end up tense in the rib-cage. In fact, trying longer just stress you up more, putting your entire body into a breathing spasm.
The advise is, in a very Singaporean fashion, relax lah.