lay on your back with your feel up and place your hands on your stomach. Say the words to your cheer but make sure you are using your diaphragm and not your vocal box if that makes sense. You should be able to feel your stomach rise when you say the words.
We practice enunciating individual letters/words. Start by having them yell their ABCs, but make sure they use a 'cheer' voice instead of a 'yelling' voice. Tell them to try to make their voices a little deeper; that usually helps with yelling from their diaphragm. Also, we do breathing exercises at every practice similar to what wcsstilldeath said, but just with breathing instead of yelling.
Tell them to project by imaging their voices being tangible things and trying to make them hit the wall furthest in front of them (if that makes sense?).
In high school we used to run laps out on our track and yell the words. It got us used to being out of breath/tired and still yelling. We also learned how to control our breathing while still being as loud as we could