Your story's exposition is where you, as the author, will provide detail and establish context purely for the reader to contextualize the story. Exposition generally does the work of telling the reader who your characters are, what they want, do, and look like, and show the environments that surround them.
Exposition therefore usually involves either explaining things to the reader as the information is given to a character—that a beloved family member has passed away, as an example—or giving details about things of which the characters are already perfectly aware, such as two characters being in a romantic relationship.
Each story requires exposition to different degrees. A sci-fi fantasy story set in a different galaxy with outlandishly named people and places is going to need a non-trivial amount of exposition or else the reader is going to feel lost and compelled to admit defeat on finishing the story. If you're writing a fast-paced story filled with lots of action in a common or familiar setting, dousing it in expository details is probably going to do more harm than good.
Irrespective of the needs of the story, exposition can still be a tricky thing to nail. Done poorly, and it can trap your reader in a mire of bland detail from which they can only escape by putting your story down—or falling into a deep slumber. Done well, and your reader should feel enticed, reeled in, desperate to continue reading and find out what happens next—they should not even realize that they've been fed exposition when they take it in, because it was perfectly natural to read.
Here are some tips to consider in your writing to get your exposition into the best shape possible, and avoid putting your readers to sleep.
Hook the reader from the get-go
If your story is going to start with some exposition to set the scene for the reader, then you absolutely must make it intriguing. Peppering the opening words with details that are going to hook the reader is vital if you don't want to lose them before things have barely gotten started.
The start of the story is normally a great place to introduce character backstories, their desires, habits and worldviews to the reader. It's also an ideal place to show the world in which the story is set.
If you can offer up this information with the right amount of detail and a lot of interest to get people set up and hooked, you can seamlessly feed your reader exposition and get it out of the way early so the main course can be served.
Leave room for intrigue
Sometimes holding back on giving all the details and instead providing hints of something more can make your exposition intriguing enough to feel like more than mere exposition. This technique is obviously a given for certain genres such as crime novels, thrillers and some horror, but any genre of writing can benefit from a bit of manufactured intrigue.
You can hand out some known information to the reader and balance it out by leaving some questions unanswered. This ought to keep your audience pining for more, leaving them with no option but to read on to find out the answers. Readers confronted with open questions are an audience that is invested in what you have to say.
Consider going back over exposition you've already written and cut out some of the information you've provided in your draft. Intentionally remove dialogue or whole scenes to prevent your writing from revealing too much too early, allowing you to intrigue the reader to continue on and plug the gaps.
Use dialogue to your advantage
Using the authorial voice to provide background and setting information to the reader has its place in literature, but having a narrator tell the audience about the story can pull readers away from the world into which you're trying to invite them. Instead, try exposition through dialogue.
There are at least two ways to create exposition through character dialogue in your story. The first is for characters to discuss information that other characters don't know. This is simple enough: write a character to be ignorant of the expository information and learn it the same time as the audience. The second way is more difficult, and involves having your characters discuss details that all of them already know. This is more difficult for the obvious fact that it can be contrived and unrealistic for characters to speak about known facts. Pulling off the second way usually means throwing conflict between characters into the mix—the dialogue is much more believable, and the reveal of information much more natural, if details such as adultery or murder (or even less sinister things) are revealed to the audience through an argument between two characters who already know these things.
However, using dialogue can backfire and you must be thoughtful in how you use it to present your exposition. The first way has its challenges in trying to not make the exchange of information between the knowing character and the unknowing character unrealistic. There's also the risk that one character comes off as a know-it-all (unless that was always your intention) and the other character coming off as too ignorant to be thought of as a fleshed out person. The second way obviously has a risk of majorly undermining the integrity of your story and characters by having them unnaturally bring up and discuss things they all know in ways that no real people would ever do.
Dialogue can be used in one other manner to deliver story details: use it to break up stretches of narrated exposition. Keeping a balance between the two can help with pacing the action and story's progress while revealing necessary information for readers to understand the context of what they're following. Squeezing even a few, quick exchanges of dialogue between two characters in between paragraphs of exposition can help keep the reader invested.
Practice and scatter it
Okay, so this one may seem like a cop-out, but practicing writing exposition is inarguably going to make it better. You can hone your exposition writing by practicing getting key scenes or information exchanges down, focusing on doing it with subtlety and as few words as necessary.
Try writing out all your exposition early on—just get it out of your system as quickly as you can: there's nothing wrong with needing to write out the backstory in drafting so you can better grasp it, and to help unlock writing the rest of the story. Feel free to use the first chapter to get it all down on the proverbial paper to let yourself finally work through the plot and action of the story.
The real work will come in editing that exposition dump and filtering it throughout the rest of your story.
Scatter details about the world and your characters at different points in your story. If exposition about a main character's parents is important, for example, try revealing the information about each of the parents at different times. Make your sentences tight, and keep the exposition sparsely separated.
Make it relevant, or get rid of it
You should only be including exposition if it directly matters to the story. Anything that's not serving that purpose should fall victim to your delete key.
If you start talking about a central character's relationship with a childhood friend, it might be tempting to start delving into the friend's full background—their parents, family's wealth, national background, location, that time they skinned their knee in primary school—but you may be going off on a tangent. If it's not serving the main story, cut it. You need to worry about getting (and keeping) the reader attached to the characters and story you're telling. Distractions and diversions can undermine that goal.
Even if you've managed to make all of your exposition relevant enough for the story, you may still benefit from going through your work and culling all the information that's been dropped that isn't working hard enough. Whatever you have left hanging around when you've gone back over your writing should be doing enough lifting to justify its existence. It should be enriching character details, conveying important themes, or progressing the plot, not just hanging about.
And if you're really going to keep exposition hanging around in your story, you need to know what it's doing and why. Anything less than that risks sending your reader to sleep while they're on the couch only part way through your story, and that's a fate few writers aspire to achieve.
