One of the best ways to memorize the Bible is to start young.
As a child, my family repeated the 10 commandments every Friday evening for worship. I never remember learning them, it seems as if they were always known. Cards with pictures for each commandment can facilitate this.
My children sometimes also held a "stone" set of the commandments, or we used felts and a felt board for each commandment.
(See below for more ways to make learning Bible Verses interesting and fun.)