There is lots of advice online – evangelical Protestants are big into memorization scripture.
I’ve done a fair amount of memorization myself over the years. I simply write out the passage on 3" x 5" cards and carried the cards with me. It’s easy to find time here and there to work on memorization. I’ve memorized a number of Psalms, parts of the gospels and epistles, even the book of Ephesians that way.
As a side note, memorization and meditation on the scriptures (lectio divina) go hand in hand. When you find a verse or passage that really speaks to you, it’s good to write it down and memorize it so you can continue to consider it. Early monks would continue to ponder scripture from their time of meditation or from the liturgy throughout the day in that way.