Select a relevant story. Say, a story about a boy who always wasted his food until he visited a poor village and saw how people there were starving. When teaching a lesson with this story, first build up the situation in the story vividly. After that, let the students or the audience discuss what they would do if they were in the boy's position. Then, you can clearly state the lesson which is not to waste food as there are people in need. This makes the lesson more impactful as it's based on an engaging story.
One way is to choose a story with a clear moral. For example, the fable of 'The Tortoise and the Hare'. The hare is overconfident and lazy, while the tortoise is slow but persistent. By telling this story, you can teach the lesson of the importance of perseverance. You can start by simply narrating the story, then ask the listeners what they think about the actions of the characters. Finally, draw out the moral and relate it to real - life situations where perseverance is key.