This is one area as a writer I am always working on perfecting.
Here are a few ways I found to introduce important background information/world-build my stories through:
Dialogue
Character thoughts
Background details
Information dump
For myself, as a children’s writer, the first two seem to work the best along with sounds and scenery description.
Two books which recently assisted me are The Secret of Nihm and The Tale of Despereaux.
I would love to know your suggestions on children’s books that helped you world-build.