A while back, I read Spiritual Disciplines For the Christian Life by Donald Whitney. Early in the book, he commends the discipline of memorizing Scripture. I had tried this in a few forms in the past and never stuck with it, but something about reading it that time drove me to commit to it.
You may be thinking, "Why would I need to memorize Scripture? I have the Bible on my phone, which I always have with me. I can look up anything at a moment's notice!" True, and I think that's great. I have a Bible app on my phone, and I'm grateful for the ability to search it so quickly. Christians throughout Church history didn't have that ability, and we live in a blessed age to have it.
But you should still memorize Scripture.
There are many reasons why you should, and many pastors, writers, and theologians have given most of them in their own posts and books (like, say, Donald Whitney in Spiritual Disciplines). But I'm going to give a few of my favorite reasons below.
It Is a Form of Meditation
When you memorize Scripture, you have a golden opportunity to meditate on it. Follow me here.
Memorization necessitates repetition. Or to put it in smaller words: to memorize, you need to repeat. Often many times. And if you want to memorize word-for-word (and, as good believers in word-for-word inspiration of the Bible—verbal plenary inspiration for you heady types—you should), you need to look closely and slowly at your verse. Read it over and over, Repeat it in your mind over and over. As you do this, you start to notice things about the verse: subtle ways the author writes, unusual word structure, words or concepts repeated earlier in the book or in other books. You start to dwell on these things.
Friends, this is what it means to meditate on Scripture.
I'm convinced meditating on Scripture is an art we need to recover. We live in a fast-paced, reactionary world that doesn't often give us time to think. Even when it does, we're so used to not having that time that we fill it with things that impede our ability to think. So isn't it truly counter-cultural to sit down and think about Scripture once in a while?
Say you've been memorizing Philippians 4:8:
Finally, brothers, whatever is true, whatever is honorable, whatever is just, whatever is pure, whatever is lovely, whatever is commendable, if there is any excellence, if there is anything worthy of praise, think about these things.
If you've been repeating it, you've solidified the order of these things in your mind: true, honorable, just, and so on. Then you can start thinking, "What is true? What does it mean to be honorable? What is lovely?" And as it happens, Paul just told us to think about these things, so we're obeying him by doing this. Good work.
It Aids in Prayer
Have you found yourself lost for words when trying to pray? I don't just mean because you're overwhelmed with how great God is. I mean because you actually don't know what to say.
Of course you have. We all have. Paul even says, "We do not know what to pray for as we ought" (Romans 8:29). So don't try to argue with me about your prayerful eloquence. You're lying.
But God gave us 66 entire books of words. And his words are perfect. Why not pray his words back to him? If you've memorized a chunk of Bible verses, you already have a reservoir of words to draw from, and so you don't need to take the time to flip through your Bible to find some. And if you don't already have words that address what you're praying for, find some, then memorize them for next time.
Meditating on Scripture also naturally leads to prayer. Take Philippians 4:8 from the last section. You've meditated on it. Maybe you've thought of some things that are true, and you've been wondering what it means to be honorable. Maybe you've been convicted of thinking about things that are the opposite, or maybe on really thinking about it some things that seemed good now don't look so good at all. You can now take the words of the verse and ask God to help you be honorable. You can repent of thinking about things that are false, dishonorable, unjust, impure, ugly, and condemnable. You can ask him to help you know truth and beauty. And you can ask him to help you obey the command to think about these things.
It Equips You for Every Good Work
Learning Scripture in any form is not just a matter of reading, nor is it just a matter of responding to God with our own words. We're meant to do something about it. "Be doers of the word, and not hearers only" (James 1:22). We were saved for the purpose of doing good works (Ephesians 2:10). And of course, 2 Timothy 3:16–17 says:
All Scripture is breathed out by God and profitable for teaching, for reproof, for correction, and for training in righteousness, that the man of God may be complete, equipped for every good work.
If we've memorized Scripture, we've armed ourselves with what we need to go out and do the good works God has called us to. A soldier doesn't go out to war with his rifle and leave his ammo back at the base. He's loaded his gun and hopefully packed more ammo. Think of your mind as the rifle, loaded with Scripture, and your copy of the Bible as the extra ammo, in case you need a verse you haven't memorized yet. I know it's odd to compare your fallen mind with a Bible, but the power is in God's words, not in the physical book (or that app we were talking about). And your mind is more readily accessible to you than anything outside of it. Why not fill it with God's Word?
Some Practical Thoughts
So how do you go about it? My basic (non-dogmatic) rule is this: one verse at a time.
In his book Ploductivity, Douglas Wilson gives the following illustration:
"The thing to take away is that brief but daily routines are capable of accumulating a large amount of whatever the work product might be. A man could take out the trash every evening, and while out there quietly lay one brick, and after six months present his wife with a brick wall along the alley—something she never even knew she wanted." 
Likewise, memorizing one verse at a time, perhaps one per day, can add up to memorizing whole books of the Bible in the long run.
You could take a short book, like 1 John. 1 John has 105 verses. Say you memorized one per day, six days per week (taking Sunday off, for the sake of a break and because you should go to church). You'd finish the book in about four-and-a-half months. Then you could move to 2 and 3 John, which you take together because they're only one chapter each.
Or say you wanted to take on a large memorization project, like the Psalms. We pray the Psalms, we sing the Psalms. Why not become so familiar with them that you can quote them or pray them anytime?
Psalms has 2,461 verses. If you took this one-verse-per-day approach through the whole book, it would take you between six and seven years to memorize it. That's a long time. But if you're around my age, and the Lord wills it, you'd probably have thirty to forty years after that where you can use what you've memorized. If you're really ambitious, you could bump it up to two verses per day and finish in three to four years, leaving you with even more time after. Not bad, huh?
If you want to memorize whole books of the Bible, I recommend reading An Approach to Extended Memorization of Scripture by Andrew M. Davis. It's a short book, and it gives a simple, practical procedure on how to go about it.
But maybe one verse per day feels like too much, especially if you're just starting out. The Weekly Discipleship Resources have a monthly memory verse. Sometimes they put two in there to keep you on your toes. Start with that. You can even stick with that. All Scripture is profitable, so even one verse per month can benefit you greatly.
Finally, maybe you feel like this is adding yet another thing to your already busy schedule. I get it. I've thought that. But I'd exhort you with two reasons to do it anyway.
First, you can, and probably should, replace something you're spending time thinking about with thinking about Scripture. I'm preaching to myself here; sometimes I'd rather do something that requires less mental power. But memorizing Scripture is good for you, for all the reasons above and more. It's probably a lot better for you than anything on Facebook, or YouTube, or Wikipedia, unless you're looking up Scripture on them to help you with memorizing it. I don't know your habits.
Second, when you've truly memorized a verse or a passage, you can think about it while doing other things. I've regularly recited Scripture in my head while driving or doing the dishes. If you're like me, you'd rather listen to a podcast or an audiobook. But it can wait. Again, I'm preaching to myself here.
I want to conclude this post by reminding you of one more reason to memorize Scripture: God will bless you for it.
Blessed is the man ... [whose] delight is in the law of the LORD, and on his law he meditates day and night. He is like a tree planted by streams of water that yields its fruit in its season, and its leaf does not wither. In all that he does, he prospers. (Psalm 1:1–3)
 Douglas Wilson, Ploductivity: A Practical Theology of Work & Wealth (Moscow, ID: Canon Press, 2020), 94.