Many meditation practices use breathing techniques to promote a state of calm. Mindfulness meditation on breath, perhaps the most well-known type, involves sitting quietly, resting or closing your eyes and bringing your attention to your breath. When your attention drifts away, which it is likely to do, simply usher your attention back to your breath without judgment. You don't need years of meditative practice to benefit from this technique, nor do your children.
There's no doubt, however, that sitting still for any length of time can be difficult for some kids. For this reason, a movement-based meditation, such as yoga, may serve as a good introduction.