When you begin talking about these themes with your child, make sure to help break down the memory verses for them. For example, when you introduce Genesis 1:1, talk about what "In the beginning" actually means. "In the beginning, God was all by Himself. There was no Earth, no sun, no stars, no kids, no toys, etc. God was the ONLY thing that existed. When He spoke the world into existence, this was the start of everything." Talk about the word "created." "Created means to make something. What kinds of things can we create?" Explain the word "heavens" and "earth" as well. "The heavens means the skies. The sky has all sorts of interesting things in it like planets, stars, the sun, moons. The earth is what we're standing on. It has mountains and valleys and dirt and sand..."
Understanding the meaning of the words they are learning helps with memorization, but it's also important to tap into a child's natural curiosities and interests. Since kids of any age are drawn to music and a good beat, a great way to help them to remember the verse is to put it to song. We put Genesis 1:1 to the tune of "Mary Had a Little Lamb." "In the beginning God created, God created, God created. In the beginning God created the heavens and the earth." It takes no time at all for them to learn a short song, and it really makes something like Scripture memory possible for even the smallest kids.
Kids are also very visual learners. You might consider drawing pictures to represent the different elements of the verse. For example, you could write a #1 to represent "In the beginning." A picture of hands could represent "God created," and a picture of a night sky and another of the earth could represent "the heavens and the earth." As you sing the song, point to the various pictures.
Using multiple senses just compounds the efficiency of a child's ability to remember. Consider making hand motions to go along with the words to the song. Making their muscle memory match their speech has a tremendous impact. Holding up their finger showing "1" for "In the beginning," pretending to build something with their hands for "God created," gesturing toward the sky for "the heavens," then jumping down to touch the ground for "and the earth" are all examples of meaningful movement to really help drive the message home.
What ways have you found to be helpful for your kids to memorize?