I wish I could persuade everyone to do this.
Here is inspiration and application on why and how to memorize Scripture.
Why Do It?
First, the inspiration.
Dallas Willard, professor of Philosophy at the University of Southern California, wrote,
Bible memorization is absolutely fundamental to spiritual formation. If I had to choose between all the disciplines of the spiritual life, I would choose Bible memorization, because it is a fundamental way of filling our minds with what it needs. This book of the law shall not depart out of your mouth. That’s where you need it! How does it get in your mouth? Memorization.(“Spiritual Formation in Christ for the Whole Life and Whole Person” in Vocatio, Vol. 12, no. 2, Spring, 2001, 7).
Chuck Swindoll wrote,
I know of no other single practice in the Christian life more rewarding, practically speaking, than memorizing Scripture. . . . No other single exercise pays greater spiritual dividends! Your prayer life will be strengthened. Your witnessing will be sharper and much more effective. Your attitudes and outlook will begin to change. Your mind will become alert and observant. Your confidence and assurance will be enhanced. Your faith will be solidified.(Growing Strong in the Seasons of Life, [Grand Rapids: Zondervan, 1994], 61).
How to Do It
Second, the application.
The most helpful practical method I have ever run into, especially for memorizing longer passages, is the booklet from Andy Davis and is downloadable here.