The more sophisticated the writing and plotting, the less obvious the exposition. But that doesn't mean there's no exposition, only that it's done subtly and carefully through the characters in a way that is consistent with the way they think, speak, and interact.
An example of subtle exposition is in the movie Lincoln, which by narrowing the focus to a couple weeks before Lincoln's second inauguration, presents an unfamiliar take on a very familiar subject. That means that there has to be exposition (there's a lot we don't know), but it has to be rendered carefully (we think we know a lot, and we'll notice any "lecturing" or "As you know, Alphonse" explanations). So what the writer and director did was to portray Lincoln as someone who likes to hear and tell stories. (This happened to be true to the historical character, but is universal enough a trait that it could have been invented without penalty.) From the start, Lincoln is shown telling stories about people he knew, people he represented in court cases. So when in the middle of a folksy story, there's a nugget of actual information, it goes down easy. It "sounds" in character.
Oppositional characters-- the opposite of attentive listeners-- are used to evoke-- paradoxically, through their opposition to the telling-- more information. At one point, a fellow Republican exclaims, "Not another story! I can't stand to hear another of your stories!" which just provokes Lincoln to grin and tell another.
At one point, Lincoln provides his own opposition. There's a particularly knotty bit of explanation needed, because we all know about the Emancipation Proclamation, and I'm sure I'm not the only viewer who was thinking, "Why wasn't that enough?" Whenever readers are going to have questions, then it's a good idea to consider giving them an answer-- but subtly. So Lincoln asks this himself, and plays devil's advocate-- it might have been unconstitutional. Or maybe it was all right during the war, but the war is ending. Maybe he did the wrong thing. He argues with himself (to an audience of younger aides), and through this conflict, we get all the information we need to answer our question, why do we need an amendment?
So: Subtle.In character. In conflict. Use opposition. Use interaction.
But there's subtle exposition, and then there's obscure. I'm reading a book now which has a fairly complex set of events leading to the characters' having to make big serious decisions. I'm at the point where one major character is going to take some major action. So two of his aides are talking. A says to B, "I hope that C will do the right thing." B gets angry, and replies, "C always does the right thing." A comes back, "Well, just tell him, we're counting on him to do the right thing."
So I read that scene, and I went back and skimmed the previous chapter, and I still had no idea what "the right thing" is. I mean, it's not just that I don't know precisely what they meant. I don't even know the basic area of what they meant. Did they mean morally? Did they mean about the staff? Did they mean legally? Did they mean about themselves?
That's too subtle. I'm a good reader, and I was paying attention. And while I'm okay with not knowing everything, I'd like to know a little. (There are about 12 major characters in this book, so, alas, I don't know enough about C even to know what -he'd- think this was.) But really, this is just a dialogue problem. A few more words here and there, and there would be enough to satisfy-- maybe not enough to make it all clear, but enough to keep me aware so that when (I hope) there's a resolution I'll know it's happening.
A says to B, "I hope that C will do the right thing about (one word, maybe? us? about the evaluation? about the account?)."
B gets angry, and
replies, "C always does the right thing. He's no (deadbeat? traitor? idiot?)."
A comes back, "Well, just
tell him, we're counting on him to (what? keep us safe? tell the truth? solve the problem?)."
That is, with just a few words-- completely in character, because we don't actually speak that cryptically unless we're being overheard, and that wasn't happening here-- we could get a sense of whether this is the staffer scared they're going to be used as a scapegoat, or if this is about some payment, or if it's a problem only he can solve. We don't need to know everything-- but we do need to know a little.
And it only takes a little. How would these two converse if they weren't being forced by their author to be obscure? They'd still be subtle. But they wouldn't be cryptic.
The reader has only what we put in there. Now exposition can be handled many ways. But if there's exposition needed, decide how much the reader needs to know, and find a way to tell it.