Children do not exist in a vacuum -- isolated from the experiences of the world -- any more than adults do. When they face trials and temptations, they need to know what God expects from them, and the Bible has something to say about any situation that comes along. The best way for your children to develop a habit of checking their actions against God's Word is to know what it says in advance. Go beyond simple Scripture memorization, though. Choose verses that directly relate to heart issues or problems that each child is currently experiencing. Ask him to write the verse on a 3-by-5 card and practice it until he can say it from memory two days in a row. Talk about why God put this verse in His book, what He is trying to say to you through this piece of wisdom and how you can use the verse to address real issues in your own life. Have him write an application statement on the back of the card to help him remember how to apply this verse on a daily basis. Collect all the verses in an envelope to use anytime this issue comes up.
Children learn more efficiently when parents model the behavior they expect. Set a habit of starting your school morning with family devotions as a sign that you put God first in your day. Christian bookstores and online retailers have many excellent devotions books suitable for children. For example, "Absolutely Awesome" by Michael and Caroline Carroll, offers a daily study of the signs of God through child-friendly, hands-on activities to demonstrate that learning about God does not have to be boring. Another option is to start in Genesis or one of the gospels and read through chapter by chapter, discussing the historical, political and social factors at play in each situation and asking how the experience of these ancient people's with God still has lessons relevant to your life today. Whether you choose a devotional book or the Bible itself, the key is to stimulate the children to think for themselves about how the lesson relates to their own lives and what God wants them to learn in this passage.
Many Christian homeschoolers worry about the wrong messages that children get from their peers, the media, popular music, textbooks and other educational materials. While the concern is understandable, parents cannot forever protect their children from influences that run contrary to their beliefs. In fact, if the children never hear about opposing viewpoints from you and run into them unprepared, your bubble of protection can fall, leaving them completely unprepared to answer challenges and more susceptible to false teachings.
On the other hand, children who are exposed to different belief systems and cultural assumptions in a controlled setting where they can compare and contrast different paradigms or worldviews against their parents' beliefs, are better prepared to own their own beliefs and stand up to the challenges that come. "The Truth Chronicles" from Focus on the Family and Tyndale's "Drive Thru History" are two resources that teach history and science from a Christian worldview to ground the children in reliable Christian teaching, so they have a solid foundation with which to compare other viewpoints and to recognize the assumptions and subtle errors that creep in unexpected places.
You may have an encyclopedic knowledge of Christian theology from the Apostle Paul to Josephus to R.C. Sproul, but if you can't explain why you believe what you believe, the smallest challenge can topple your house of cards, calling into question everything you were once so sure you believed in. As a responsible homeschooling Christian parent, you do not want to let this happen to your children. From a young age, they can understand, if presented age-appropriately, that Christianity is not just a pretty set of nicely told fairy tales or random collection of ancient stories with no real scientific proof. Science and religion are not mutually exclusive endeavors, as some would have it and a careful examination of the facts with an honest and open mind reveals many clues in nature as to God's hand in the creation and ordering of the universe throughout history. Two books that help illustrate this for children are "It Couldn't Just Happen: Fascinating Facts About God's World" by Larry Richards and
"Don't Check Your Brain at the Door" by Josh McDowell and Bob Hostetler.