To get your diaphragm going, pant like a dog out of breath. Put your hand above your waist. Now, laugh—when you laugh you are actually breathing through your diaphragm. It's like a large band all around this area of your body. To exercise your diaphragm, lie down with an object like a heavy book pressing against your chest.
Practice: Raise the book up and down and get used to breathing through your diaphragm. When you're standing, practice not lifting your shoulders as you breathe: Proper breathing isn't seen or heard by your audience.
It's not just how you take in air, but how much. If you take in too much, you are going to flood your diaphragm; if you take in too little, your voice will sound very thin. You have to learn to distribute air evenly over an entire sentence, and it's a good idea to take in a little extra so you don't run out of steam. Because the most important point usually comes at the end of a sentence, you'll want to have enough energy to really make your point there.
Get into the habit of taking air in through your nose and letting it out through your mouth; this way your mouth doesn't get dry, which is a common speaking fear. Breathing through your mouth will only accentuate whatever dryness is already there.