When I started writing Duality, I had in mind this almost dystopic setting where there were 5 major cities--the locations of the 5 laboratories--and everything else had just gone to crap. For my world's purposes, science had replaced religion as the opiate of the masses, and the government invested more in the labs than in its citizens. Because the action takes place mostly in the labs, I had to include this information in spurts, but avoid "As you know, Bobs," which was especially tricky given my MC's amnesia. So a couple of things Dima asks about, and I have a few opinionated secondary characters. I try not to info-dump.
For example, there's a scene where Dima's watching the lab workers unload cargo for the next round of experiments. As the workers unload the human components, she spots a stringy-haired kid in ratty clothes, covered in dirt:
"He was a gutter-rag, a kid who lived on the outskirts, not in one of the major cities. He represented the most impoverished section of America, and now he was being led like a lamb to slaughter."
She doesn't go into a diatribe concerning which cities were the major ones (because she might not remember), but she gives you enough insight into how the people who live outside those major hubs are treated (like they don't even matter). Here's a second example:
The PTSD. The missing leg. His desert-scented fear… The Oil War. The government had thrown him into a useless battle with the Saudi nation for garbage oil that couldn’t even be refined effectively enough to pad the country’s thinning supply. Even though it had ended years ago, he looked like he was still in it.
She doesn't discuss how the War started or ended, only that it occurred and had affected the person she's thinking about.
In other parts of the story, Dima might be testing her memory, thinking about what she might or might not remember. It's possible to weave in bits of history creatively without it being overbearing. What I try to do is focus on my world as my MC knows it rather than as an outside observer. That helps to avoid info-dumps and "As you know, Bobs."
But how do you know what to explain to your audience and what not to? That primarily depends on your main character. Is your MC an alien in the world you've created? If so, then he's not going to know much about what's going on, and in informing the MC, you inform your audience. One of the best examples of this is the Syfy series Eureka, which follows Sheriff Jack Carter as he tries to maintain peace in a town of super geniuses building stuff for the government. Here's one of the more entertaining quotes showing what I mean:
Allison: Now that we are involved I had to file an IA248 with the DOD
Allison: It's the form required for our intimate alliance.
Jack: There can't be a form for that!
See what I mean? Jack doesn't know what an IA is, and Allison tells him without giving too much info, like why the form is required or when the forms first came into use. Just enough info to answer Jack's question.
The thing to remember about world-building is that, even though we as the writers need to know EVERYTHING about the world we're constructing, the readers DON'T. The information they need should be given in context with the characters and situation.
If you guys have questions, leave them in the comments, and I'll try to answer them in the next post.