To make it easy for your readers to share your stories, you can add a Twitter (and Facebook) share button to your story via the social tab in the story-editor top toolbar:

 ...or by clicking where the social buttons appear in the header of the story in the editor.

The resulting panel enables you to specify a Twitter card image, the share text that will populate the tweet when the share button is used, a via Twitter handle to be referenced in the tweet as the source of the story, and a short version of the story's URL, to be placed at the end of tweets instead of the full URL.

If the story is going to be hosted on your own servers (rather than with Shorthand Hosting), you'll also need to provide the full URL of where the story will finally be published so that tweets from your story can include the appropriate link to it.  Add the story URL via the editor's settings tab: