On Exposition in Literature
In the context of fiction, exposition is writing intended to explain something - some detail of the setting, a plot point, a character's background, or anything else that needs to be told to the reader. Expository dialogue can be a tricky subject - it's not exciting, it can be very mockable if done badly, and yet many stories depend on it. You can avoid the worst of it through careful planning, but even the best of us need to know how to execute it well.
We'd all like to think that we can write a complete novel without having to feed information to the audience, and yet all but the simplest stories are going to need it, simply because there are things that can't come up naturally in dialogue. Backstory, for one - whether you're delving into character motivation or the lore of your setting, you'll need to explain that which you can't show. Very complex plot points - including things like the wrap-up at the end of a mystery - call for a healthy dose of exposition. And there may even be times when you actually want to insert some expository dialogue, simply because a good speech can really show off a character's personality.
So let's delve into exposition in all its awful glory.
Narrative Expository Styles
How you've set up your narrative will determine what your exposition looks like. How much does the POV character know from the outset? Who's going to do the explanation? These facets of your style will have a big impact on how you write expository dialogue. Before we look at the tricks of the trade, figure out what style best suits your story.
Fish Out of Water
This is an especially common style, one that has appeared in works of fiction spanning many generations and genres. One character - typically the protagonist, but rarely a secondary character attached to the main POV character - is the outsider, naive to the plot and setting, and expected to learn what's going on from everyone else. The obvious strength is that the author can use this naive character as the stand-in for the reader, who learns along with the protagonist. It's an easy fit as well, appropriate to any setting in which the lead character is new on the scene.
Passing the Baton
This is a team variant on the above style, requiring at least two significant characters from very different backgrounds. One character serves as the guide, with the other(s) playing the "fish out of water," but they switch out these roles as they pass from place to place. This is a somewhat uncommon style that's probably best suited for epic works or series fiction, where the group will cross through a variety of settings.
The New World
This is another style for groups, but in this case everyone is a "fish out of water." No one is clued in to what's going on, so everyone starts from a position of equal ignorance, though some characters may know more by the end of the story. While this style opens up some interesting possibilities for character interaction and growth, it is a pretty rare style that's only suitable for a narrow range of stories - particularly those themed around exploration and/or with a grand scale mystery as a significant plot element.
This is the exact opposite of "The New World" - everyone understands the setting and plot from the word go. Without a reader stand-in, the author must put across all relevant exposition through dialogue, context clues and - sparingly - expository gimmicks. While this results in very natural storytelling, it's also far and away the hardest style to do well, as the reader can easily become lost. Definitely a style for experts only.
How do you put across information? There are a lot of little tricks and methods authors have used to avoid didactic explanations. It's best to be cautious here - none of these tricks are definitively bad, but they are easy to misuse and age has turned them into cliches.
At a crucial point in the narrative, a character finds a document that reveals some hitherto unknown piece of information. Use of epistolary elements is common across all forms of fiction, but it's probably best known in the "files" used by video game developers to introduce worldbuilding and backstory.
It's worth remembering why video games employ this style - in most cases, "files" are not critical to the plot, so a player who's bored by lore can safely ignore them. A novel reader won't have that option, so make sure that your own documents are not just interesting, but plot relevant and introduced in a natural way.
So it's come to this - one character sits everyone down and explains everything that's going on at length. No one likes the infodump - it's an especially artless and painful form of exposition. However, for more complex stories, there are times when an infodump is a necessary evil because some plot element is too big to put across through hints and context.
If circumstances force you to employ an infodump, there are a few things you can do to keep the suffering to a minimum. Keep your exposition on point and as short as you can - none of those fifteen page speeches that self-published writers seem to love so much. Don't use an infodump to paper over a plot hole - you have the editing process to fix those mistakes. And for the love of all that's holy, keep your personal opinions out of it. No one likes to be preached to.
The Basil Exposition
This is the infodump made flesh, a character who seemingly exists for no other reason but to explain things to the protagonist. Again, you might have a situation where this character has to exist because there's someone who's just more knowledgeable than everyone else. Even so, you should take care to limit how much of the plot is revealed via this character.
At the extremes, I've seen stories where the Basil Exposition explains everything in the plot and thus the protagonist never learns anything for himself, something that sucks the drama right out of the story. If your own narrative is developing in this direction, one solution is to find some pretext to remove Basil Exposition from the story for a few chapters. Having the lead wander blind and do his own work for a while will do him - and you - some good.
Hidden Clues and Red Herrings
And now for something different - let's talk about lying to your audience. There's a long history in literature of misleading the reader by presenting false clues and/or keeping vital information out of sight. Using either will entail adding more exposition, as eventually someone needs to explain to the reader what was going on.
Tradition aside, these tricks can easily upset the reader, and that's never a good thing. There are two things to keep in mind to help you avoid this. First, always be fair - your reader should be able to at least make an educated guess as to what's going on before you explain it, so don't conceal/fabricate so much information that this becomes impossible. Second, hidden clues and red herrings should always be organic to the story. That is to say that these tricks should make sense inside the setting and should never exist solely to flummox the poor sap who opened the book (unless you're angling for postmodern, I suppose).