Lectio Divina ('divine reading') is only slightly more involved than the technique of contemplative prayer. The physical mechanics are almost identical to other meditation techniques. The primary difference is that in the previous exercise you have a single word that is repeated (to the point that any thought of meaning is lost and attention is focused on the simple act of repetition), but in lectio divina the meditator has chosen a phrase from the bible to read repeatedly while considering closely the meaning of that text.
Historically, the Psalms have provided much material for this Christian technique, but really any book in the Bible will have plenty of useful verses. Taking a well known Psalm as an example, we can look at Ps. 23: "The Lord is my shepherd, there is nothing I lack. In green pastures You let me graze, to safe waters You lead me; You restore my strength. You guide me along the right path for the sake of Your name. Even when I walk through a dark valley, I fear no harm for You are at my side; Your rod and staff give me courage."
Once the meditator has established a quiet space (as in contemplative prayer), he or she can quietly read through the chosen verse. Initially, the thoughts and impressions which arise as a result of mindfully going through the lines will be pretty generic, surface level material. That's fine. It's how our minds work.
But as the practitioner of this Christian meditation technique continues to read through and really begin to taste the meaning of the text, the message begins to morph from a general statement written to billions of people scattered over thousands of years into a message spoken just for the reader. The message becomes a message of love from God sent directly to His child.
In that frame of mind, the meditator can begin to allow the words of the message to fade from awareness. However, instead of an absence, a simple sitting and resting with God can be experienced. When speaking of meditative experience we are often stuck using metaphorical language to describe it; in this case, the feeling engendered by lectio divina is not unlike the felt experience had by the small child who has been running around, laughing and playing (maybe even getting into a bit of trouble). Finally acknowledging his exhaustion and coming to his mother or father, he climbs into their lap, and simply rests in that secure embrace. In this case, we are the child and God is our loving parent who wraps His love around us.
Through both Christian meditation techniques of contemplative prayer and lectio divina, the expectation is that, over time, this repeated exposure to spending restful time in communion with our Father will produce wholesome changes in our spirit: unruly passions like anger and greed will wither, while healthy impulses toward compassion and a desire to fulfill God's will in our lives grow. I address the usefulness of that assumption in other writings, but it is clear that either or both of these practices can make a powerful impact on the spiritual life of the Christian willing to explore them.
For more information on Christian meditation check out Christopher Boozell's website http://www.TantricChristianity.com. You can even sign up for a free mini-course on meditation!