In Home Education, Charlotte Mason writes about scripture memorization (page 253 of Volume 1). Her words are in bold:
Bible Recitations.––The learning by heart of Bible passages
should begin while the children are quite young, six or seven. It is a
delightful thing to have the memory stored with beautiful, comforting,
and inspiring passages, and we cannot tell when and how this manner of
seed may spring up, grow, and bear fruit; but the learning of the
parable of the Prodigal son, for example, should not be laid on the
children as a burden. The whole parable should be read to them in a way
to bring out its beauty and tenderness; and then, day by day, the
teacher should recite a short passage, perhaps two or three verses,
saying it over some three or four times until the children think they
know it. Then, but not before, let them recite the passage. Next day
the children will recite what they have already learned, and so on,
until they are able to say the whole parable.
Three months ago, after realizing my toddler had memorized more than a few Veggie Tales silly songs, I decided to try scripture memorization.
The first verse I chose was Psalm 100:3: Know that the Lord is God. It is He who made us and we are His. We are His people, the sheep of His pasture. It answers the question "Who made you?" - one of the truths a toddler is ready to learn. (For more on truths children are ready to learn, check out The Spiritual Growth of Children. This book was a gift from my aunt and uncle, and it's a wonderful resource.)
All I did was write the verse in marker on a piece of paper and tape it to the wall. Every day, I read the verse to her one time. After two weeks, she had it memorized, stopping me to recite it herself. "No no no, Mommy. I'll do it."
For February, I repeated the same process with Psalm 23:1: The Lord is my shepherd. I shall not want. Again, she quickly learned it.
During February, if a block tower fell down, or Mommy or Daddy told her no, my daughter would cross her arms and say, "I can't do anything." I knew what verse she needed to memorize in March: I can do all things through Christ who strengthens me. - Phillipians 4:13. Now, I know this verse does not mean that all of the block towers we build will stay standing, or that Mommy and Daddy will let us do everything we want to do. But it has stopped her from saying "I can't do anything." It has also hidden in her heart the truth about contentment. And though we can't tell when or how this truth will bear fruit, we know it will.