This is by far the best resource (short and to the point) for learning how to breathe for better singing results, and it starts with Brett Manning's 7 secret breaths which he outlines in this video.

Another huge part involves your diaphragm.

Your diaphragm is bellow your rib cage. And the biggest distinguish that singers need to make is that breathing for singing, is not the same as breathing for speaking.

Aaron does a great explanation about this difference, and gives you guidance on getting better at controlling your breath. Mastering this will help you find your range and hit those high notes.