How to Overcome Worry: Experiencing the Peace of God In Every Situation by Dr. Winifred Neely is a short, practical guide to dealing with worry and anxiety. Based on a sermon Dr. Neely preached out of the book of Philippians, How to Overcome Worry is a great resource for Christians dealing with what can be a confounding topic.
Dr. Neely equates anxiety and worry, which he defines as, "concern turned inward and deformed, divorced from the grace of God and rooted in unhealthy fear" (pp. 29-30). He makes the helpful distinction between worry, proper concern, and clinical anxiety, noting that concern is appropriate, and a normal part of life and clinical anxiety is the result of living in a fallen world.
Using Paul's letter to Philippi, Dr. Neely provides tips to overcome worry. Keeping one's focus on God by using prayer and scripture meditation, Dr. Neely says that we can find God's peace which, "is the awesome well-being, the glorious serenity, the inexpressible wholeness, and the inner tranquility that characterize the infinite being of God Himself" (p.68).
As one who has dealt with anxiety, I found How to Overcome Worry extremely helpful. It is practical, biblical, and doesn't trivialize or dramatize the subject. It is short and easy to read, and is a great resource for Christians dealing with the topic.