A bad storyteller could tell a crowd the most exciting news piece of the year (the breaking of a 108 'curse,' for instance), and put his audience to sleep. A good storyteller could talk about a trip to buy a package of napkins, and hold his audience's rapt attention.
It isn't the story that makes the story good, worth reading, interesting; it's the storyteller. When he starts to tell a story, he resumes the responsibility to guide, to entertain, to make the audience feel like they didn't waste their time.
In light of that responsibility, how do you become a better storyteller?
#) Practice. It's the number one advice for getting better at everything. You don't get better unless you try. Trying takes time. Practice telling your story—develop your craft. Try different words different places, use bold expressions, make dramatic story-telling moves that you're scared of. Tell your story in the mirror. Tell it to your mom (and then someone who loves you a little less, for more critical feedback), tell it in the dark, tell it to the flock of birds at the pond. The more you do it, the better you'll be.
#) Watch/read/listen to other people. It's hard to develop a craft well in complete solitude. The lucky thing about developing your art is that sharing is allowed. If someone else does something that you admire, that's completely brilliant, try it. Tweak it, change it, make it yours, but don't be afraid to grow by imitation. Other people come up with amazing strategies. Using them isn't wrong—it's like adding a tool to your tool-chest.
#) Say what matters. In this busy, flustered, over-worked and under-rested society, people only want to listen to things that matter to them. If they don't see any reason to listen to what you're saying, they won't listen. Think about what people want to hear, think about what matters to them. They want to hear virtue, kindness, human triumph through herculean struggle. They want to hear stories that make them cry, or roar with laughter, stories that end with a warm feeling all over, or the bright resolve to be a change in the world, to make a difference.
#) Pay attention to your audience. If they're not paying attention, or you're not getting any feedback, if 7 of the 12 people are sleeping, maybe it's time to reconsider how you're telling your story, and change things up.
Being a storyteller is a privilege; being a good storyteller is a gift. Appreciate the privilege and the gift, and do your best to be better. The world could use more of those people (us).