Yarn. It is an informal word for a story, often one that is spun or told quickly and might be a bit exaggerated or humorous. For example, sailors used to tell yarns about their adventures at sea. These were usually quick, engaging stories.
Recounting. This means to tell someone about something that has happened. For instance, when a witness recounts the details of a crime in court, they are actually telling a story of what they saw and experienced.
Narrating. For example, when you are narrating an event from your life, you are essentially telling your story in a more organized and often sequential way.
Account. It can mean a report or description of an event or situation, which is also a way of telling a story. For instance, when someone gives an account of their travels, they are basically telling a story about their journey.
Well, 'raconteur' is also a great word. A raconteur is someone who is really good at telling stories in an engaging and often vivid way. They can hold an audience's attention with their tales, whether it's a short anecdote or a long, complex story. In a literary context, a raconteur - like character might be the one spinning the yarn within the story, much like a narrator, but with a bit more charm and flair.