I just saw this from Mark Driscoll of Mars Hill Church and I think it's GREAT info. I thought I'd share it.
Step 1. Eat dinner with your entire family regularly.
Step 2. Mom and Dad sit next to one another to lead the family discussion.
Step 3. Open the meal by asking if there is anyone or anything to pray for.
Step 4. Someone opens in prayer and covers any requests. This task should be rotated among family members so that different people take turns learning to pray aloud.
Step 5. Start eating and discuss how everyone’s day went.
Step 6. Have a Bible in front of the parents in a translation that is age-appropriate for the kids’ reading level. Have someone (parent or child) open the Bible, and assign a portion to read aloud while everyone is eating and listening.
Step 7. Parents should note key words and themes in the passage and explain them to the kids on an age-appropriate level.
Step 8. Ask questions about the passage. You may want to begin with having your children summarize what was read—retelling the story or passage outline. Then, ask the following questions: What does this passage teach us about God? What does it say about us or about how God sees us? What does it teach us about our relationships with others?
Step 9. Let the conversation happen naturally, listen carefully to the kids, let them answer the questions, and fill in whatever they miss or lovingly and gently correct whatever they get wrong so as to help them.
Step 10. If the Scriptures convict you of sin, repent as you need to your family, and share appropriately honest parts of your life story so the kids can see Jesus’ work in your life and your need for him too. This demonstrates gospel humility to them.
Step 11. At the end of dinner, ask the kids if they have any questions for you.
Step 12. If you miss a night, or if conversation gets off track, or if your family occasionally just wants to talk about something else, don’t stress—it’s inevitable.
Adapted from “Family Dinner Bible Studies” by Mark Driscoll in Trial: 8 Witnesses from 1 & 2 Peter, a study guide. (Mars Hill Church, 2009), pages 69-70.