John Piper has published a letter he wrote to a 13-year old girl that wanted to go deeper in the Scripture. His suggestions:
1. Read the Bible as a whole. Use a Bible Reading Plan like the Discipleship Journal plan to keep track of where you are reading.
2. Focus on some unit of Scripture to go deeper.
You might want to do this through memorization.
Or write that section out long-hand.
3. Get a good study bible like the ESV Study Bible and use it.
4. Pray as you come to the word: Incline my ear, Open my eyes, Unite my heart.
Share this with your children. Read the whole thing.