Recounting. When you recount a story, you are giving an account of what happened. It often has a sense of going through the events in the order they occurred, like when you recount your day to someone.
Narrating. It's a common alternative as it directly refers to the act of telling a story, often in a more detailed and sequential way.
'Spinning a yarn' is also a way to say telling a story. It has a more informal and perhaps even a bit of a creative or fanciful connotation. Sailors used to spin yarns (tell stories) about their adventures at sea, often with a touch of exaggeration to make the story more exciting.
Storytelling can also be called 'recounting'.
Weaving a tale. It gives the image of carefully constructing a story, much like weaving a fabric. Each element of the story is like a thread that is carefully put together to create the whole.
Some other names for telling a story include 'chronicle - making'. This is like creating a record or account in the form of a story, often with a sense of historical or sequential order. 'Fable - speaking' can also be a name, especially when the story has a moral or a lesson, like traditional fables. And 'anecdote - sharing' is another, which is more about sharing short, interesting stories from personal experiences or things one has heard.
Narrative, tale -telling, story -sharing.
The four words could be 'narrator', 'point of view', 'voice' and 'perspective'.
First-person narrator, Third-person omniscient, Multiple narrators, Stream of consciousness.
Some common French transition words for telling a story are 'ensuite' (then), 'puis' (then, after that), 'après' (after). These words help to connect different parts of the story and make the flow more smooth.
Relates. Such as 'She relates an interesting anecdote.' It implies sharing a story or event in a connected way.