The only “correct” way to write is the way that works best for you. Some write longhand on a tablet. Some outline, draft, outline again, then fill in the blanks. Some write the ending first then work their way toward it. Some write sequentially though I swear I don’t know how they do it! Stephen King begins all his stories with a single thought. “Wouldn’t it be funny if…” For example, for his novella “The Mist” he thought “Wouldn’t it be funny if huge bugs attacked a supermarket?” (yeah, the guy has a warped sense of humor!)
My personal style is to listen. For example, I was walking downtown recently when I saw a street sign at an intersection. I was on 17th street, but the only marker for the cross street was a “one way” sign. And I suddenly heard a voice say “I live at the corner of 17th and One Way.” The voice was middle-aged, female, and quite British. I tried to figure out who said it, why it was important, and what the townsfolk thought about the lady who lived there. It’s one of my best stories!
Oh, also, I don’t really write. Even this answer to you – my fingers write. If I couldn’t type I’m not sure I’d be much of a writer, because most of the time they tell the tales. I sometimes feel as though I’m just along for the ride!