Teaching a moral through a narrative story is a long-standing literary device dating back as early as Aesop. Narratives demonstrate their morals in a way that personalizes the lesson for the readers, making it a more powerful teaching tool than lectures. How you approach the core concepts of moral within your narrative will strongly affect how effectively the story teaches your intended lesson.
Emhasize Expected Outcomes
For a lesson in a narrative to hit home, it must contrast with expected outcomes. Although a story with an expected ending can still carry a moral, it will not be as engaging or memorable as one with tension and surprise. For example, "Beauty and the Beast" would not as effectively sell the idea that appearance isn't everything if not for the expectation that Belle would marry the beautiful, successful human being. When writing your narrative, touch on known themes, archetypes and popular stories to underscore the expected narrative. This will make the twist ending and its attendant moral all the more powerful.
Use Simple Characters
Some of the message in a narrative work is carried by the story, but much is carried by the characters. "The Tortoise and the Hare," for example, derives as much of its message from the personalities of the title characters as from the circumstances of their race. Although other forms of narrative writing often benefit from complex, nuanced characters, fables work best with simple, unambiguous characters, often characters that are simply representations of the core ideas within the moral. This keeps the focus on the story and its lessons, rather than on the characters themselves.
Discuss the Moral
If the point of your narrative is to impart a moral lesson, it's important to discuss the moral clearly. Aesop's fables did this by literally ending the tale with a quotable line that spelled the moral out. Other fables, such as George Orwell's "Animal Farm" and O. Henry's "The Gift of the Magi," don't separate the moral from the narrative, but emphasize it in the end lines of the work.
Write for Your Audience
Different morals and different narratives are more or less appropriate for different ages. The short, animal stories with a simple lesson of Aesop work well for elementary-aged children, but are less appropriate for teens and adults. Stories for teens and adults will impart their message better if they star human beings having realistic interactions with more complex ethical issues.