What is the point of writing a story, and what are the key elements you must include? How do you come up with an idea, and how do you develop the idea?
Wow, what a loaded question to lead with! The point of writing a story is to communicate with our fellow human beings some relatable experience, whether it be an internal or external one. It is an opportunity for both author and reader to connect on a universal truth. Aristotle, in his work Poetics, notes that the point of all art is to achieve a catharsis, or a purgation of emotions, that is accomplished through consuming a piece of art that one finds especially poignant. He says that this is accomplished through imitation, so it is the responsibilty of the author to accurately represent the subject of the work.
They key elements of a story are character and plot. Think of a story, regarless of length, as a complete sentence: it needs to have a subject and a predicate. The character or characters of a story are representations of the author, the reader, or someone else entirely. We relate to them and become interested in their story. The plot is the progression of the story. A story has a begging, middle, and end so the reader feels relief or some other emotion because of the story's resolution. The rest -- setting, tone, genre, medium, etc -- are all prescribed by the characters and the plot.
I personally come up with ideas by consuming other media. That's not to say that I steal from other people or anything like that. Instead, I take inspiration from other works and artists. I try to re-frame my own experiences in life and make them universal and relatable to people who aren't me. I develop these ideas by writing them down and seeing what shape they take as I'm writing them. I don't typically do a lot of planning on my short stories; I mostly let the characters dictate where the plot goes. To write this way, however, requires unwavering confidence in your knowledge of your characters. You really need to know everything about them to know how they'll act.
I hope this helps, and good luck with your writing!