Learn your story not by heart, but with your heart! Traditional tales have been told for generations, each teller changing and adapting the tale to meet the needs of the time and the audience. Develop your own version of the story you wish to tell.
Consider how you feel most comfortable learning other things and apply this to how you learn stories. You may find one method works better than another or you may like to use a combination of learning techniques.
Some people have a good visual memory, they learn by creating a series of pictures in their head or storyboarding on paper. Oral memory is strong in others who find it easier to remember a story by hearing it. Others prefer the written word, or learning key points/facts.