Each month, I have my daughter (age 3 1/2) memorize a new Bible verse. (We've been doing this since January, so we are now on Month 12.) For now, we do one a month, and all I do is read it to her once daily. After hearing it repeated several times (the number of times depends on the length and complexity of the vocabulary and syntax), she's able to recite it herself. This month's verse is the first verse on our Advent Calendar - Isaiah 9:1. She had this one down in three days. It's short, and I think it helps that she's able to decode words now and knows several sight words so she can read along.
The people who walked in darkness have seen a great light.