Limit your descriptions. When you're writing detail and description, try to focus on the one or two key features of what you're describing, and only describe the things that need describing. For example, in a literary fiction book you might see a description of a living room that details the faded wallpaper, the retro furniture, the ancient television, and the worn carpet before focusing the antique grandfather clock that strikes midnight. In an action/adventure story, you can save words by focusing on what's really important in this room: giving it a dated feel, and the grandfather clock. Rather than an entire paragraph of detailed description, you accomplish the same thing with a sentence that quickly establishes the tone of the room and immediately focuses on the clock, the most important aspect of the room.

Steamlined dialogue. Dialogue is a remarkable element that can either take up a lot of space, or save a lot of space, depending on how you use it. A lot of banter back and forth can take up hundreds of words in a story and get you nowhere. By contrast, a carefully crafted conversation can convey a ton of information that would take paragraphs of prose to explain. By meticulously working smart dialogue into a story, you can save a ton of space and keep things moving along at a brisk pace.

Fewer or no subplots. With short stories in particular, there's often not enough space to deviate very far from the main story/theme you're trying to get across. In order to properly set up and pay off a subplot, it requires a lot of work (and a lot of words). In a short story, you may not have the luxury of spending that many words focused on something other than your protagonist and his or her main conflict. In longer works, you can still run into the subplot problem if they don't feed into the main narrative in some way, ideally all coming together in a big, active conclusion rather than requiring individual resolutions.