The Catholic devotional tradition has long been helpful in making us aware of our many layered-universe.
But how do we learn that? A saint might say: "Meditate and pray long enough and you will open yourself up to the other world!" A poet might say: "Stare at a rose long enough and you'll see that there's more there than meets the eye!" A romantic might say: "Just fall in love real deeply or let your heart get broken and you'll soon know there's more to reality than can be empirically measured."
And the mystics of old would say: "Just honour fully what you meet each day and you will find it drenched with grace and divinity."