This is the greatest thing that any horror story can achieve, it is also one of the most mind-numbingly difficult things to do. Of the horror movies which have achieved this coveted state, I will state only a handful have truly done so. For whatever reason, possibly because people need to use their imagination more, I'd argue horror literature has an easier time of achieving immersion. I'll still list my top three immersion examples from movies, though, because they're references people can immediately get an idea of what I mean from.
Jaws, of all things, is the probably greatest movie success for building immersion. No, people didn't believe the events depicted on-screen actually happened but they believed Great White Sharks were capable of killing people. The tourism industry as a whole suffered that summer and the author of the book devoted rest of his life to preserving sharks due to the hysteria he inadvertently helped create.
Prior to Jaws was Orson Welles 1938 radio drama broadcast of the H.G. Wells classic, The War of the Worlds. Even before the internet was invented, Orson Welles managed to successfully troll a substantial portion of America. However many were actually fooled is anyone's guess, probably not as many as would be cinematic, but enough that it obviously had an affect.
Finally, more recently, there was The Blair Witch Project where a lot of gullible Americans were fooled by the idea of found footage. Less gullible Americans still appreciated the attention to detail that went into making the story plausible if not believed.
Most modern-day horror films, I tend to think aren't actually horror per say. They're action or fantasy features which just happen to have a higher gore count than what is expected by audiences. Routinely, after seeing a bunch of his buddies slaughtered, the hero rallies back and defeats the monster in the end.
Evil is punished. Yay.
Horror novels have been known to follow this standard as well, perhaps because a downer ending is something audiences are disinclined to accept after a lengthy period of bonding with a main character. No one would doubt The Shining is a horror story but, spoilers, it ends with at least two of the characters getting away at the end. Short-stories, by contrast, tend to have a much higher body count as the pressure to have it end on a high note is less.
Really, I think true horror is something that's surprisingly difficult to achieve. It requires the audience member to be a willing participate in putting on their suspension of disbelief. They must accept that not only is a guy in a painted Captain Kirk mask wielding a knife but said individual is going to kill someone the audience cares about. Psycho by Alfred Hitchock predates Halloween and managed to turn people off showers for years thereafter.
How does one achieve this, though?
Honestly, I have no idea. Still, I'm going to make a couple of guesses. The first is establishing people in your work are human beings. Stephen King made his living creating quirky New England towns filled with people who were, more often than not, strange but believable. In fact, I'd argue their quirks were what helped sell them to the audience. No person in real life is completely normal. Bob might be the most average American male of all time but his obsessive love of Woody Woodpecker well into adulthood makes him more like someone we might know.
Once you're able to establish the people involved in the story are human beings, making them act like them is a difficult task. One of the chief flaws of zombie films nowadays is the fact that everyone in the world should be familiar with how zombies work yet it's not like they were ever a folklore monster. Zombies, as they exist in Hollywood, are solely the product of movies. Plus, if you have people lamp-shading the zombie-threat, you run the risk of making the story tongue-in-cheek.
A good rule is to think about how you would react in a given situation and build from there. If there's a serial killer in my house, I am getting the [censored] out of there. If there's aliens, it's going to take a little longer for me to wrap my head around the situation since I don't believe in them.
Blind panic is possible but should happen after a very specific set of circumstances. Gory deaths might work but, really, I imagine most of us would be numbed by just sudden death around us period. Assuming we're not trauma surgeons, EMTs, or battle-hardened soldiers.
Next is to take the audience out of their comfort zone completely. One of the most effective ways of doing this is, ironically, starting in it. The shower scene in Psycho is so effective because we're at an extremely vulnerable state when we're bathing, especially if the curtain is closed.
One of the most effective elements from the Marble Hornets series is the fact Slenderman routinely appears in cameras unnoticed by the main characters. The lurking dread something is right behind you, which you don't see, is a very primordial fear. If you can convince your audience a threat is coming into their house with impunity while they're asleep - you've got them.
Finally, taking the audience out of their comfort zone leads me to think there's two really effective ways of achieving horror with monsters. The first is using very believable monsters and the second is using ones which are utterly incomprehensible. Monsters which split the difference by being fantastical but well-known manage neither.
The problems with vampires is, as H.P. Lovecraft observed so very long ago, they're rather well-known. People know what to expect from a vampire and the horror is diminished. It's part of the reason we rarely see ghost stories nowadays, because people have gotten it into their heads they're nonthreatening. There's too much Casper and not enough Poltergeist going round.
Believable monsters are monsters which can exist in the so-called real world. Cujo the rapid dog is a terrifying construction because he's something which could happen in real life. Norman Bates the schizophrenic/dis-associative identity disorder serial killer is unusual but not impossible. Misery is insanely effective because the villain is just a person with absolute power over our protagonist.
Unbelievable monsters are the opposite in they are completely incomprehensible. One of the most effective short-story ideas I ever got but couldn't turn into something concrete was a man found himself completely unable to leave his hometown, nothing supernatural at first, he simply became overwhelmed with panic attacks at the border of the town.
Then he discovered everyone else was in town and no one could enter without becoming effective. What's causing it? Hell if I know, I didn't finish the story but the tension for the mystery and powerlessness makes it good. Likewise, a monster which never communicates and simply does things can be quite effective. Ditto beings with abilities we don't understand unlike the vampire.
I'd hesitate on describing special effects, however, because horror and awe are enemies. If I found out my front door suddenly lead to a vast Stygian abyss, there's potential for horror there, but there's also a certain level of cool that might work against you. To achieve the desired effect, you have to use the wrongness of a door opening to nowhere against the reader. This is achieved in Peter Cline's 14, almost word-for-word.
These are just my thoughts, hope you enjoyed them.