After a panel at Comic Con, I had a question about worldbuilding in short fiction. There both wasn't much time to answer, and I was fairly beat after the end of a long (and awesome) con. Here's a much better answer.
There are four techniques that jump to mind for effective, succinct worldbuilding: interweaving and multi-tasking.
Interweaving: This is the opposite of the dreaded info-dump. Instead of cramming all the information the reader needs into one paragraph, it's parsed out bit by bit in the text. Information feels less "info-dumpy" when it's only a sentence long, especially if it's in the characters POV.
Multi-tasking: This applies to novels as well, but especially in short fiction, a sentence or a paragraph can't do just one thing. It can't just be for setting, or worldbuilding, or character, or to advance the plot. If it's not doing at least two things, it probably needs to get cut or get revised. Three things would be even better.
Point of View (POV): This goes hand-in-hand with interweaving and multi-tasking. Those snipits of info should still sound like they're coming from your viewpoint character. And if your worldbuilding info is in its proper POV, it's also multitasking to show you character.
Concrete Details: Of course you don't want to toss clunky descriptive paragraph at the reader, but the right, specific noun can suggest a truckload of information. The restaurant serving fillet mingon over a bed of organic microgreens is not the same one dishing out Kentucky hot browns. Detail after carefully selected detail can imply a world richer and fuller than the one your character has time to explore.
On to examples! Here's the first scene in my novelette, "The Temple's Posthole". I'll dissect it below. This scene is exactly four hundred words long: