It's different for every story, but generally the best way to get a lot of information across is to show it. If it's a poor neighborhood, don't tell us it's a poor neighborhood. Show us the cracks in the streets, the peeling paint on the buildings, and the closed shops with broken windows. Basically, just get the big picture you want to tell us in your head, then think about the symptoms that describe what you're trying to tell us.
One mistake that a lot of writers make is that they feel like they have to get their entire world across in the first chapter. In other words, they don't space the information out. A good rule of thumb is, if it's not relevant to the story right away, you can put off showing us the information. This rule doesn't always apply, but what I'm trying to say is spread the information out. Don't clump it together or else your reader will feel overwhelmed.
I've run into this problem with a side project I recently took up, for a different fandom. I've already started writing the story's beginning, which consists of two prologues that each focus on the backstory of a different character, and some themes that will recur in the story later on. But they're meant to be entirely self-sufficient, almost like one-shots, so all the vital information I want to convey has to fit into the respective prologue it belongs in. The problem is... it's a lot of information. The first drafts literally had several straight pages of nothing but info-paragraphs, which contained either worldbuilding, or detailed the characters' thought processes over a long period of time, which I couldn't express in any other way than through just explaining them. With time, I managed to dilute the information a little using dialogue and action (showing, not telling, as was said earlier), but the result is that both prologues are roughly 26-27 pages long, and still incomplete. I expect they'll pass the 30-page mark when I'm done.
Normally I don't have any qualms about writing long chapters, but this particular story has gotten me to worry for the first time that I'm giving the reader too big a mouthful. Since these two chapters are prologues, literally every piece of information in them is important to the story, and oftentimes as I was writing, I completely put the page count out of mind and wrote until I had described every tiny detail of the world I wanted to build -- which includes a detailed description of important locations, events that span across several years, history, and relationships. And I want to make sure that the reader registers and understands all of those details, because I won't be able to explain the same things again during the actual story. The most I'll do is allude to them, and even so, subtly.
My main worry right now is that, even without many of the giant text-blocks I had earlier, the prologues are still like giant infodumps, so packed with content that, inevitably, some things will slip from the reader's mind. Or worse, as they're reading they'll get dismayed that after half an hour the scrollbar is still halfway down the page and stop reading. Hopefully that's an exaggeration.
Has anybody run into the same problem before? I'd love to hear your thoughts.