Breathing is a major part of mindfulness and meditation, and there are fun and simple ways to introduce this key calming skill to children.
There's a technique called breathing boats (also known as breathing buddies), which helps children to physically tune in to their breath. Ask the child to lie down and imagine they have a boat resting on their belly. Ask them to breathe deeply, right down into their bellies as they breathe in, and notice how their imaginary boat is riding the waves up and down with their breath. They can imagine any thoughts that come into their minds as bubbles that float away.
In the Breathing Buddies version, you actually place a physical object on their tummies — a small stuffed toy, for example.