The most important thing to remember about writing a scary story is that it needs to have suspense and a spooky mood.
Suspense is the term we use for interesting things that happen in a story that make you want to read more. When a story has suspense, the reader is interested throughout. You can create suspense in some key ways.
First of all, foreshadowing is a very useful tool to create suspense. Consider this quote from Poe’s scary story “The Tell-tale Heart.”
I was never kinder to the old man than during the whole week before I killed him. (see first link)
This one line creates all kinds of interest. We know there is going to be a murder, and we wonder how it will happen. We also wonder about the narrator’s sanity.
Another good way to create suspense is through setting. You know a good scary story begins on a dark and stormy night. A scary story has a scary setting. In “The Monkey’s Paw” by W.W. Jacobs, the spookiness of the setting was established early on.
"That's the worst of living so far out…of all the beastly, slushy, out-of-the-way places to live in, this is the worst. Pathway's a bog, and the road's a torrent. I don't know what people are thinking about. (see second link)
If you set your story in a uniquely scary place, half of the work is done for you. Setting helps to establish the mood (the emotional landscape of the story), or the idea that there is something spooky going about. Both of these stories establish a mood carefully at the beginning.
I heard all things in the heaven and in the earth. I heard many things in hell. How, then, am I mad? Hearken! and observe how healthily—how calmly I can tell you the whole story. (see first link)
You will want to use words that are spooky, scary, and moody. Words like “dreary” and “mad” can be used to engage your reader and really make your story scary.