When you're talking about breathing in singing, the most important thing to do is to remember to breathe. It's very easy in the middle of a song, especially if you're emotionally invested in the song, to forget to breathe, then you get to the big high note and you have nothing left.
Some great exercises to make sure that you're connected to the breathing is to, I like to do one where we're actually lying down. What lying down does is it stops you from worrying about supporting your skeleton. We all have a lot of habits that are bad habits that we've cultivated over a lifetime of walking around. Whether you're a person like myself who tends to carry a lot of shoulder tension or you're a person who tends to put a lot of weight on the front of the feet, you want to think about posture; bringing it back, keeping it relaxed, keeping the chin down further than you would normally keep it.
A lot of us do this; this creates a lot of tension in the throat. If you have yourself standing straight, relaxed, the head is in a neutral position, you're ready to start the breathing. Then a simple exercise you can start out with is lying flat on your back on the ground, let everything fall away. When you're lying on the ground, you'll feel all of the pockets of tension you have. You want to let all of that go. Then you just want to put your hands on your lower abdomen and take some great, deep breaths. I want you to pay attention and notice, and make sure that the top of your chest isn't moving, too. It should all be coming from down here. If you take a breath in and this happens, then what you've done is you've taken a shallow breath; not great for singing, increases the tension in your throat, and you won't have enough to get through.
One big, good breath is worth a lot of little, tiny, shallow breaths. That's the most important thing that you want to think about when you're breathing during singing.