1) Start late in the story. Let's say you're writing a 300-word horror story about a guy who dies in an alligator attack during his honeymoon. There's probably not time to show the wedding ceremony, the reception, the plane ride to Florida with his new wife snuggling sleepily against his shoulder... Instead, you might want to open with the man walking hand-in-hand into the swamp with his new wife, an avid bird-watcher, who is hoping for snapshots of a rare Florida egret. Considering starting just before the story climax, the most exciting point in the story (the alligator attack, in this case), so that you'll have time to do it justice.
2) Stay focused. In 300 words, there is no space for anything that isn't essential to the story you're telling. If our alligator attack story were a novel instead, you might take some time out to tell the reader some interesting history of Everglades National Park, to give some background about the birds the soon-to-be-widow is trying to capture with her camera -- or about the species of alligator that's trying to capture her unfortunate husband on its teeth. When you're writing very short stories, you can't afford scenic detours -- you have to stick to the path (as our unfortunate hero should have done).
3) Choose the right details. If you want to create the effect of a detailed picture but don't have room for a lot of details, the trick is to choose the right ones. Choose details that suggest the rest. The fact that our doomed hero's hotel room has a king-sized bed, two dressers, a desk, and a desk chair doesn't paint a mental picture of any specific place. A burnt-out fluorescent ceiling light does -- this is not the Ritz. An ugly hotel hotel room and an alligator attack -- our poor hero!