The two kinds of development you might choose to employ in your short story are rising action and progression toward a new understanding. These are very different, but can sometimes be found in the same short story.
Rising action is action taken to solve a problem. In this type of story, action is the result of obstacles which are encountered. The protagonist usually fails to resolve the problem immediately (it's not much of a story if everything just gets better). A good example of this is an infection running loose in a hospital. The protagonist must work quickly to contain the infection before it spreads to the general populace. A time limit helps to make the action rise faster. In a short story, this time limit is often necessary to avoid turning the short story into a novel.
Progression toward a new understanding involves the psychology of the characters. Conflict arises from the interaction of the characters, often enhanced by outside forces. The characters of the short story are pushed and prodded toward realizations, changes, or breakthroughs of a psychological nature. An example of this type of plot development might involve a mother grieving and depressed after the loss of her child. An unexpected visitor might arrive, jarring the mother out of her depression and allowing her to move on with her life. Not a lot of action, but a powerful story nonetheless.
These two can sometimes be combined, but if you're writing a short story, be wary of doing so. The traditional length of a short story is 3000 words, but never more than 10,000 words. With so few words to work with, you might find your short story quickly becoming a novella or even a novel. If you don't mind ending up with a longer story than you originally intended, then experiement with different approaches.
