If you want to build cardio and leg muscle endurance quickly the Army does 60/120s and they are great for that, also great for burning off fat. You sprint as hard as you can for 60 seconds straight then walk for 120 seconds, rinse and repeat. Do that at least 10 times. Although in basic training they do 30/60s instead to start off light so may want to start off with that.
Another simple breathing trick while running is to breathe in twice before you exhale, it trains you to take deeper more efficient breaths.