I'd like to add the the diphragm breathing. (sorry can't spell) I've been to many vocal coaches and done the whole book on the belly, and making your belly big thing. Guess what neither one really works that well, if at all, to learn breathing for singing.
the abdominal muscles expanding out are a secondary reaction, they are layered over what you are trying utilize.
When you say expand your abdomen or suck it in, the majority of people, myself included use the abdominal muscles instead of the diaphram. What happens is it looks right, but you still aren't getting proper breath support.
One vocal coach pointed out something too me. the diaphramatic muscle has more surface area connection to the chest/rib cage at the lower /BACK RIBS and sides of the ribcage. So, why does everyone obsess over the front?
This is how he had me do breathing for singing, and it is the first time it made my voice project and become dramatically louder and take tension off my throat.
1. Breath in like a wide yawn, the adams apple drops and it open the throat. Breath goes in naturally. Don't puff out the abdomen like a fat budda belly it actually tightens up your throat. Just let it expand naturally. don't expand your upper chest it really shouldn't move much.
2. as you breath in concetrate on expanding your lower back ribs.
3. As you breath out/ sing out concentrate on squeezeing with the lower back ribs almost as if you are pushing your ribs forword through to your front. this is where very high pitched singers get awesome power. You will notice as you do this that the front part of your abdomen sucks in as your diaphragm goes up and supports your voice.
Now it not only looks like it should, but actually does what it's supposed to.
All without you thinking about it or flexing your abdominal muscles. That's another thing DO NOT FLEX your six pack it will hinder the diaphram.
Another thing he taught me was that laughing can teach you proper breathing and help get you started. Do a quick laugh, it shoots your voice right out of you because your diaphragm is pushing it out. You should also notice you feel it, guess where, your lower back ribs.
After using this breathing techniqe for singing my voice was marketable louder and projected with no throat pain.
Word of warning though if you have never sang using the right breathing, the first couple of times after a 2 hour set you abdomen can feel like you just did a whole mess of crunches because of the secondary reaction of the abdominal muscles.
but, at least your throat won't hurt.
Of course after that you have to know how to sing on pitch and focus your resonance for tone shaping. Whole nother story though............