We best understand stories when we are inside of them rather than they being outside of us. How do we enter stories?
It isn't about us entering stories. It is about the quality of the story, that draws us into the experience. It's the hook that starts drawing us in, and the pacing and plot that pull us deeper. I found a series that does that very well with "The Wandering Inn." The world has depth to it. The MC is an idiot in many ways. Most of what hooked me on it was the idiot MC, what dumb thing would she do next, and how would she get out of it. She is dealing with a variety of different races, each with a distinct culture. The seemingly minor culture clashes, cause her problems in her ignorance.
I took your question as an active event by the reader. Rather that passively being drawn in by the story.
I would say the best way to pull readers in, is the premise. The What if, of the story. And a compelling hook.
I think there are many ways readers can be drawn in (I agree with Mister Bogart that it's got to be done by the writer, the readers aren't responsible for attracting themselves to your story). Some are drawn in by emotional poignancy, some by fascinating philosophical or scientific ideas, some by mastery of language, some by a well-structured story, some by elves and dwarves, and on and on. Character and character interaction (aka drama) are definitely some of the ways, and probably among the most effective and powerful. For me personally it's the beating heart of story, next to vivid setting. Characters are the gemstones, the setting is, well, the setting, and they must complement each other. But it's the dramatic interaction of those characters that's the real draw (for me I mean).
This is how I enter a story, too. This suggests a related question: what part of the reader enters the story? What inner hearing of the reader does a good story reach, what vital part of the reader?
One of the big things that can draw me in is the world. It has to have depth to it, and effort put into it. The where or when don't matter much. I have seen too many books where the world reminded me of the painted sheet an elementary school might use as the background for a play. and those get tossed back on the shelf, in short order. The world conveys elements of the culture, which helps shape the characters. If an author didn't put effort into his world, then how much effort went into the characters? It reminds me of the early SciFi authors, Asimov and Clarke had some pretty two dimensional characters, but the science kept you reading.
I heard an interesting exercise restated the other day on a podcast. it was the old rewriting a scene from a book three times, but the twist they put on it was changing the POV, even suggesting the family dog as the POV for the exercise.
That would be an interesting challenge. Stretch your writing chops. But you'd have to anthropomorphize the animal somewhat if you wanted your reader to relate to it.
