How to breathe into your stomach and not get light headed during meditation?

During conventional Buddhist sitting meditation I have a problem whereby because I am thinking about my breathing my breath is quite short (I can't seem to change that) and just a few minutes in, just as I am starting to get into a deeper state and see something, I find that I start feeling quite light headed and almost hyperventilating because I am thinking about the breath and thus not breathing as I usually (which may still not be the perfect way for meditation, but at least normally when I'm not thinking about my breath I don't hyperventilate). I have been told by teachers that I should try to breathe into my stomach as this is good energetically and will make the breath to the degree and the length it needs to be. However, no matter what I try, I don't seem to be managing to achieve this stomach breathing. So I was wondering if there is a particular knack to it or any advice? Am I actually trying to breathe into my stomach or just to expand my lungs down there (different teachers have said contradictory things on this matter)?