Decide what the horrific element of your story will be. Horror typically involves something supernatural, such as ghosts, vampires or monsters. However, you can also create a horrifying character that is all human, such as the character of Leatherface from "The Texas Chain Saw Massacre," by adding an extra-frightening aspect to him. You want to create a villain that your hero or main character has to come up against and fight to stay alive, or to stay sane.
Develop your protagonists. Make your main characters just as interesting and complex as your horrific villain. Come up with believable characters by creating a background for them that lets readers in on their insecurities. Did their parents die at a young age? Were they abandoned as children? Deliver a main character and supporting characters that add to the story and help you to build on the plot.
Come up with a basic idea of the journey your characters go through in discovering this horrific entity and fighting it. If there is no struggle between the two forces, your story can get boring and readers won't want to read. Whether you place your main character in a haunted house or force him to fight an evil alien on a distant planet, you need to come up with a struggle.
Write your story by using a basic outline of the plot points. Perhaps your main character has just bought a haunted house. You don't want to give away all the horrifying elements of the house right away. Use foreshadowing and suspense to build the horror until the climactic end, when the main character has either fought the evil and won, or the other way around.
Read your story. Let others read your story, too. Decide what works and what doesn't. Maybe a description of the horrific element does not quite horrify; tinker with it until it truly comes across the way you want it to. Maybe the ending does not completely satisfy; brainstorm to find another ending that adds a twist to shock the reader, but one that also works with the story. One of the most important parts of fiction writing involves editing your work until every aspect works together to truly engage the reader.