A well-told story capture the audience and remains with the people long after the other details of an event are forgotten. Here are some suggestions for you to improve your technique:
Have a great beginning
Start with simple stories and then get more adventurous as your skills grow.
Head for the children's library for all sorts of examples of folk and fairy tales that you can adapt well to any context.
Remember that when you tell a story, the focus is on you. Practice and live with your story so that when you perform, you can command the audience's attention and take everyone with you. Know the first lines and last lines by heart and simplify the structure to a few key points.
Tell a humorous story with a deadpan serious face and you can make much more impact than when you smirk all the way through. The element of surprise is powerful.
Hold on to that essential ingredient of rapport to keep people listening.
Arrange the time, place and setting in which you tell the story. Make sure that people are relaxed and comfortable. Campfire setting and flickering log fires make for perfect storytelling moments - as do seats under shady trees on lazy summer's day.
Think of your voice as a well-tuned musical instrument. Notice how your breathing affects your voice and practice a range of sounds and volume. Enjoy exploiting all your skills to perform to the full range of expression.
See what you can discover from other people's stories and the way they tell them. You may adapt parts of their stories to make them your own or notice how they work with their voices, the audience and the stage.
Speaking from the heart rather than reading from a book or script is more powerful...and people allow you to be less than word perfect.
Stimulate your audience's senses so that they can see vivid pictures, hear the sounds, get in touch with feelings, even smell and taste the delicious tale your presenting.