Start with something scary.
The most important thing for a scary story is a scary subject. And I don't mean 'Eek! Spiders!' generic-type of scary. Monsters with blood red eyes too many teeth might be superficially scary, but there isn't much thought put into them. Plus, they're really only scary on the outside - and giant spiders will only scare people who are, of course, afraid of spiders.
Instead, close your eyes and think about what scares you. Terrifies you. Something that, if it happened to you - you're not sure you could recover.
"I'm scared of being alone."
"What if I got into an accident and became paralyzed?"
"No one's ever going to fall in love with me."
"I think I'm being replaced."
"What if I disappear someday, and nothing changes? No one cares that I'm gone?"
"My parents are probably going to die before me."
Thinking about these might make you uncomfortable. You'll want to push them away, think of something else - and that's how you know you're on the right track. I guarantee, if you find something you're truly, deeply scared of, others will fear it, too.
Then, think about why it scares you.
Go into the gritty details. Say you're scared that your loved ones will hurt you. Why? What makes being killed by your loved ones worse than being killed by a stranger in a dark alley? Pin down the really scary bits.
"You're scared of the dark? Why?"
"...What's in the dark?"
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Lastly, use these fears to spin stories. Say, again, you fear your loved ones will hurt you. This could be as realistic as spousal abuse, to unrealistic as your husband coming after you with an axe. You can play up the paranoia factor by, say, having a story featuring an online stalker, and slowly discovering that the person doing it is someone close to you.
Or, you can make it supernatural. A Monkey's Paw scenario where your friend gets wishes granted, but each time it brings chaos down on you - and for some reason, they keep doing it. Or, a shapeshifter is in your house, and your dad has been acting kinda suspicious lately...
The best way to do horror is to build up, too. Slowly. Don't jump right into BLOODY WRITING LIGHTS FLICKERING HOWLING ON THE HORIZON sort of thing. Build up to it. Let the protagonist suspect something is awry, brush it off, then suspect again - then make the terrible things happen. Sometimes it's effective to let the protagonist 'win', escape the monster, only to have it catch up to them in the end.
Tips for writing:
Use sensory detail. Not just sight, but touch, sound, smell.
Don't explain everything. Sometimes, it's ok if the protagonist never finds out what, exactly, is scratching behind the wall, there. Even if it's been leaving them messages.
Have a good ending line. It's such a downer when a horror story just peters out; a good, solid line is like turning a key in the lock, when everything clicks into place.
And, Read it to others. You're a terrible judge of your own work. The best way to test if something is scary is, naturally, to test it on a friend.
(Just make sure they like horror first.)