Scripture memory has a long history. Before the printing press, it was one of the only ways most Christians could have the Word as their own. It still is important for believers today, especially as we battle the constant stream of spiritually draining media content.
I think all believers should be memorizing Scripture as a part of their devotional life, and I have a few tips. I'm no expert, but these have worked for others in the past.
1. Make a plan: If you want to memorize a large chunk of Scripture, it's key to have some kind of strategy to make sure you don't get discouraged or bogged down. It's important that you balance progress with your schedule: making a plan to memorize 5 verses per day may not be sustainable. I recommend memorizing a verse or two every couple of days. It's difficult to memorize anything in a day, but working on a small section every day will pay off with lots of progress over time.
2. Find accountability: It can be very helpful to find someone to memorize with. It's not so much about studying together, thought that can help. Accountability keeps you honest and helps you not quit when things get tough.
3. Establish a routine: We all know that regularity is key to changing our behavior patterns, and Scripture memory is no exception. If you've already got a daily devotional or quiet time, I recommend adding 10-15 minutes of drill time to that. Don't feel bad if that cuts into your usual Scripture reading time. Think of Scripture reading and memory as exercising different spiritual muscle groups. Just like at the gym, some times you focus on one area to the neglect of others, that that is okay as long at it is done with balance and with prayer.
4. Use tools available: You know from your school days that there are many memorize material: listening, writing, flash cards, etc. It may take time to find what works for you. I encourage those who are technologically inclined to try an app I've found called Verses. It uses different kinds of drills in one easy interface.
Of course this whole process ought to be bathed in prayer. I believe the Holy Spirit helps us memorize Scripture in a way that is beyond our actually abilities. This is a difficult task, but it's ability to transform our lives is well worth the effort.