Horror evokes many emotions; dread, fear, paranoia, suspense and terror. So why not try your hand at some nightmare fuel evoking stories? Note that not even this can make you become the next Poe, Lovecraft or King. Try to learn a bit about writing stories first. Write A Story is a good place to start, and perhaps reading some horror stories would probably help.
To Start OffBefore and during writing, thinking these questions is a good idea.
Who are you trying to scare?Despite horror being a known genre today, that doesn't mean all types of horror will scare everyone. If you want to scare kids, don't make it as blood-curdling as you can. If you want to scare adults, don't make it as tame as you can. Try to find a balance.
Is this just a story or is this trying to be realistic?Again, not every horror work will scare the hell out of the reader and make them call for their brown pants. Some people may laugh at a zombie apocalypse story that tries to be scary. Do you want to fool people into thinking this was real, or stick with Zombies Everywhere Issue #14528: Electric Boogaloo? Keep in mind that both kinds can be scary, so don't go into writing describing everything in great detail, and have a paranoiac writing Madness Mantra all over the walls.
How are you trying to scare them?This one is very important. There are many ways to disturb someone to the point of frequent nightmares. There are many things that writers use:
Supplemental ReadingImmersion and Horror by C.T. Phipps at The United Federation Of Charles discusses how to get your audience prepared to be scared.