There can't be a universal answer to this, I think, since different people like different kinds of stories. However, it helps if you get things clear in your own head beforehand. Imagine how you'd tell the story to somebody else. This way you'll eliminate confusion (e.g. "Oh, I'd forgotten to say that the guy lived on an island and had a huge dog!") and boredom - nothing worse than starting out like "Two years ago we went to Italy. Er, no, actually, it was three years ago, because two years ago we were in Spain. Or was that last year? Anyway..." by which time you'll already have lost your audience.
It's usually best if your story has a point or punch line. You need to identify this and work towards it. For example, if you want to tell a story about an exceptionally strong and hard guy who faints at the sight of a drop of blood, then don't start out by saying "Isn't it funny how the strongest, hardest guys will sometimes faint at the sight of a little blood?"
I'd suggest to keep an eye on good storytellers and see how they work. Depending on what type of stories you wish to be good at, you can find a lot of TED talks, stand-up shows, book readings etc. to give you an idea what it takes.
Besides the mastery of how to tell a story, you'll also need to be sure that the story is worth telling. How long should it be? What's the punchline, the details you need...?
If you find a good story, you can practice it over and over again to perfect your execution, before using it on your friends, or at a party or presentation.
Practice makes perfect!
So, if you like stories, and like to tell stories, you may create your stories as often as it possible!
But, be careful! Don't think about what is interesting to you personally, but about what is interesting to your audience!