There's more than one answer to that, so I encourage all my writer-buddies to jump in and offer their own strategies in the comments.
Here's my attack:
The Big Picture
1) Stories are about people, even if those people don't happen to be humans. Your main character, at the very least, needs to be someone the reader can relate to.
That usually means your protagonist needs some moral grounding, some intelligence, and some depth. Personalities that are too extreme, in any direction, don't work well in the role of protagonist. (They're great as secondary characters, however.)
2) Stories are about change. The story begins when the protagonist's life swings out of balance. Their actions thereafter are about trying to get their life back to normal.
They never really succeed, however. The events of the story must leave the protagonist changed forever, otherwise it's not a story.
The Meat In This Sandwich
1) Conflict and tension are what make a story gripping to a reader.
1a) If you keep implying that fireworks and mayhem are about to happen, the reader will happily plough through another 400 pages to see everything blow up. Tension is the sense (either to the reader or to the characters in the story) that the situation is escalating.
Tension can be completely internal and emotional, by the way. The promise of heartache and angst is just as powerful a way to keep the reader turning pages as the promise of giant robots punching each other.
1b) Conflict is when there's a struggle between two entities to trying to reach mutually exclusive goals. This is usually between two characters who want different things and are acting to get them, but a single character also can be internally conflicted if they want two things but can't have them both.
2) Empathy is what makes the reader care about what happens in the story.
The best way to make the reader care is to show them how much your characters care. If your protagonist is in distress over the events of the story, that emotion helps drag your reader's emotions into play.
The Nuts and Bolts
So how do you actually take an idea and setting and then turn them into a story?
First, figure out what the conflict is (or can be.) What is going wrong in this world? How are people going to be hurt?
Second, create a character who (1) will have their life thrown out of balance by these events and not like it, and (2) is able to act to try to restore the balance.
This person is going to be your protagonist. Their struggle to swing their life back to normal forms the body of your story.
Why? Because stories are about people, even when they're also about something massive like the end of the world. You need to focus on people, usually one person--your protagonist.
Your protagonist has a problem (their life is out of balance), and they're trying to fix it (by reaching a goal, something they think will help re-balance their life.) Now you need to give them obstacles; you want to make it virtually impossible for the character to get what they want.
And you want your character to care about that. It should cause them distress to not be able to reach their goal. They might be angry, sad, anxious--there are really only two emotions in the world: pleasure and pain. You want your character in pain.
Because that will cause the reader to empathize with them.
I explained in this post what I think you do next:
You have the protagonist act. They choose to do something they think will get them closer to their goal, but events conspire to give them something other than what they expected. Often, those events make the situation worse.
So the protagonist must act again, this time more courageously, and again things go wrong. You keep doing that until the character has been traumatized enough that they finally find the inner strength to overcome all remaining obstacles, reach their goal and fix the problem that started the whole story.
There're a few last things to consider:
Every scene needs:
1) Conflict (at least two forces in opposition)
2) Tension (the sense that things are getting dire, or that they won't work out)
3) Emotion (one character must care about what's happening in that scene)
4) A turning point (a moment where things change irreversibly)
You want to consider how many possibilities for the above four things you have while you plot out a scene, but you also want to keep those four things firmly in mind while you write the scene, too.
Without conflict and tension, you won't hold the reader's attention. Without emotion, the reader won't care about the story or its characters. Without a turning point, the scene is wasted space--turning points are the moments when your story steps forward, and those are the only moments that should be included.
Again, I'll invite my writer-buddies to share their expertise in the comments. How do you take an idea and turn it into a living, vibrant story? What do you think are the essential elements? In your view, what's the most important 'big picture' thing to keep in mind? What's the most important 'fine detail' thing?
Are there some things you refuse to think about until you actually start writing, or do you plot out every nuance ahead of time? I'd be honoured if you shared your wisdom with us.