Have an interesting story to tell. The key of storytelling is to provide listeners with a good story. If you don't have a story worth listening to, no one will listen. Focus on your audience. You are definitely not going to tell a horror story to little kids! Just like you shouldn't tell an overly childish story to older ones. Find a good story for the listeners.
Memorize the basic story. If your story has dialogue, you don't need to memorize the exact dialogue, just the basics.
Use hand motions to emphasize the story. Doing so will catch a listener's attention plus make the storytelling exciting. Hand motions should be incorporated when the tale calls for it. For example, if a line says "The tree was taller than the sky," you could point up.
Use facial expressions. If a character in the story is sad, for example, frown. If a character is happy, a smile would work. Pay attention to the mood of the story, as well. Let the mood flow into your expressions.
Allow your voice to be expressive. Give the characters different voices. If the mood in the story is scary, low tones are perfect. Build your voice at the exciting parts, then drop it suddenly right before the most exciting part. In a simple fairytale, focus on your audience. If your audience is young children, use kind voices. Older kids may enjoy a more funny telling.
Add details. A girl with brown hair and blue eyes could be described in your story as a young girl with golden brown hair and eyes as blue as a river. Exaggerating small things in a story can give a wow effect.
Practice in advance. Before you tell your story, give it a try. You may want to videotape yourself or do it in front of a mirror so you can see the flaws in your telling. After you watch the video of your telling, mute the sound so you can only pay attention to the visual aspects. Did you use hand motions? Check your expressions as well. Now, close your eyes and just listen to the story. How is your articulation? Did you use "ahhs" or "ums?" Adjust the telling based on what you notice.
You might want to use props, images or toys to add color to your story. This can also be useful in addressing sensitive issues as it deflects attention from you, the storyteller.
Practice telling your stories to a non-expert. Does it make sense? Does it achieve what you hoped?
M. Clough (2010).The Story Behind the Science: Bringing Science and Scientists to Life in Post-Secondary Science Education, Science & Education (2011) 20:701–717