Horror, unlike fantasy or science fiction, is a little bit harder to as a table-top game. The GM has to be careful when building that sense of dread and terror and one wrong step can cause the whole concept to crumble. Also, if the players are not willing to buy into the concept and play along with the concept, the game will quickly unravel (This is true for any game really, but its especially true about horror games).
Now, let's say you've thrown the idea out to your players and they seem interested. You have an adventure in mind, but you're nervous that you might fail to deliver on the horrifying elements and the game might end up being a complete dud. Well, there are a handful of elements you can focus on that will you run a successful horror-themed game (or let you add some horror elements to your existing game if that's your goal). Those elements are Mood, Mystery, and Tension.
Mood is probably the easiest of the elements to capture. When describing a location or setting up a situation, focus on the elements that would make the location or situation creepy. For example, let's say your characters are traveling down a country road that leads to an abandoned mansion one of the characters recently inherited. To set the mood for the horror to come, you can focus on the isolated nature of the country road and the derelict nature of the mansion. Describe how the floor boards creak underneath their feet and and the only source of light seems to be the sunlight slipping through the tattered curtains. Focus on those details that will help create that sense of dread and uneasiness that will get your character's on edge.
Creating a sense of mystery about things also helps as well. Basically, its working on the "Less is More" idea where the less you know about something, the more mysterious and creepy it can be. For example, lets say your characters go into the basement of this mansion and you know there is a ghoul warren hidden underneath the house. When they finally encounter these ghouls, you could call them by name, but that takes away the mystery of the creature. Instead, only describe them physically. Call attention to their gaunt frames and pale flesh, their talon-like fingers and rotten teeth, and the stench of carrion that hangs around them. Keep the characters guessing about the true nature of the creature, what its motivations are, what it will and won't do, why exactly is this thing here, how long has it been here, and so on. While the characters can discover these things as they play the adventure, the mystery should still be there and you should use it to add that fear of the unknown.
Finally, remember to build tension to make the moments of horror more effective. For example, we have the ghoul warrens underneath this abandoned mansion. The characters discover a trap door in a cellar that leads to the warrens. Now, you could have them open the trap door and two ghouls pop out and growl at them, but that's not scary. Instead, you drop hints about what might lie beyond this trap door. You mention a few scratch marks on the door and the ground surrounding it, and a faint rotten smell hanging around it. When they open it and drop down into the warrens, you mention how the stench seems to grow worse the further they delve, and bones litter the floors of the cave. As they draw closer to the ghouls, tell them they start to hear the sound of something eating, tearing and clawing away. All of these elements help build the tension that will be released when the ghouls spring their attack. It, like mood, will help put the players on edge as well.
While there are other elements you could throw into the game as well, like taking the normal and twisting it into something abnormal, the three above elements are the most important in my opinion. Focus on them, implement them, and build upon them to help make your horror games better.