I can not stress this point enough! To tell a story you must know all the aspects of it, you must know the story line, characters and conversations 100% by heart. Now, this does not mean that you have to memorise every word of the story and tell it exactly how it is written, because the main point here is that you must know it by heart, not only by mind. In my opinion, if you tell the story 100% according to the script, you could just as well be reading a book. And for me that is something entirely different from being a storyteller.
When I find a good story that I want to use I firstly read it through several times, then I make a short list of all the characters and important points in the story line and this list is what I will learn by heart, the rest is improvised while telling the story. But what I do next is to close my eyes and visualise my self telling the story for an audience. I’ll repeat the visualisation until I know the story by heart. And for every time i visualise this the story gets more detailed.
Using this technique means that a story will never be told the same way twice. There will always be slight changes to it and this is what makes your stories evolve from the script to something that is your own.