I actually don't have much experience writing straight-up horror, but I have written about horrific creatures in my fantasy stories. I also love playing up the fear aspect. So here's what works for me.
You really have two options for creating something scary. Either the thing itself is scary, or it's mundane and twisted in a way to make it scary.
The Thing Itself is Scary
In any kind of monster story, the creature itself is scary. People are scared of zombies, aliens, ghosts, and satanic cult leaders. Focus on what makes the "thing" scary. What's scary about a zombie? How it's rotting? How it moves? Or is it the fact it was once a human being? And we can become one? Often what's scary about aliens is that they are so different from us--we don't understand them. So with aliens, it's often the unknown we fear. Some "things" are intelligent and have motives and can plot, so they are scary because they are cunning. Others are scary because they don't have sound reason--you can't predict what they'll do; you can't reason with them.
Figure out what's scary about your "thing" and focus on that. Can you put your characters in a situation that shows us how that rotting zombie moves awkwardly and attacks without reason? How can you make your aliens even more alien? Brainstorm a plot that best illustrates your thing's scary factors.
The Mundane made Scary
Some of the scariest "things," aren't things at all. They're everyday people, everyday objects. Often what’s really creepy is something normal that has been twisted, distorted, or perverted. Look at clowns or toy dolls. They were once entertaining and fun until horrors twisted and perverted them--now almost everyone and their dog thinks clowns are scary.
When I was a child, I once got into my head that evil dolls like Chucky could get me through mirrors, if I looked into them. So, suddenly, I developed a mirror phobia. The worst part was that mirrors were everywhere.
So this technique can be powerful because it can effect the readers long after they finish your story. To learn a little more about this tactic, you can check out my past blog post: Writing Creepy: Perverting the Normal
Non-thingsI should point out that sometimes what's scary isn't an object but a situation. Being stuck on a ship that's sinking near the south pole is scary. Getting lost in the Australian outback is scary. But like I mentioned earlier, find ways to illustrate why it's scary. Show us that your character is suffering from severe dehydration in the outback with no water in sight. Focus on it so that readers really feel the seriousness of the situation. These examples fit into "The Mundane made Scary," because they take innocent situations like sailing a boat, and twist them to make them scary.
Presentation goes a long way in writing. Zombies might be terrifying in one story and hilarious in another. It's all about the presentation. So take the time and put in the work to describe the "thing" or situation right. The best way to get a reader to feel something is not to focus on the emotion (in this case fear), but to focuses on what elicits those emotions. For example, compare these two passages:
Harry saw the dementor and it terrified him. He could never remember being this scared in his life. Fear swallowed him. He was scared, and he didn't know what to do.
Where there should have been eyes, there was only thin, gray scabbed skin, stretched blankly over empty sockets. But there was a mouth…a gaping, shapeless hole, sucking the air with the sound of a death rattle.
By the way, I made up the first example. But look at the second one. Instead of J.K. Rowling telling us how scared Harry is, she describes the dementor in a way that will make her readers feel fear themselves. She perverts what's normal "Where there should have been eyes, there was only thin, gray scabbed skin, stretched blankly over empty sockets." We all have eyes, but what's creepy is that while the creature has sockets, they're empty with skin over them. Look at the words she uses: "gray scabbed skin," "empty sockets," "a gaping shapeless hole," and "death rattle." Each phrase is creepy. She uses words we associate with sickness and death and deformity.
Pick creepy words to describe your "thing" or situation. The better you describe it, the more fear your readers will feel.
Thanks for asking, and good luck!