Read the story and allow yourself some time to reflect on it before starting your paper. Read for plot and exposition -- the who, what, when and where of the story. Note anything that puzzles you or that doesn't seem to make sense.
Look for answers and clarification on a careful second reading. At the same time, look for symbolism and motifs in the story. Symbols may show up as objects, actions or even colors. Motifs are repeated images, phrases or other elements. For example, in Michael Cunningham's "White Angel," white is a motif. It appears throughout the story, either as a color or as something that is white, such as snow.
Ask yourself what the story is about thematically. It may be a story of grief or of human resilience or any number of traditional themes, such as man's inhumanity to man, good versus evil, or man against nature, which is often a story of pride, or hubris. Explore how the symbols and motifs fit into the theme.
Look for those characters who have changed or not changed by the end of the story. Consider why a character changes or does not. If a character changes, try to pinpoint at what moment the change takes place and what caused it.
Write out one or more theses that you think you could argue based on your reading and evaluation of the story. List facts that you could use to support your thesis idea. When you know you can develop several main points, drawing support from the text, you have a viable thesis. If the text does not support a thesis, you won't be able to make a successful argument. For example, both planes and UFOs are mentioned in "White Angel," so you might want to argue that the planes are really flying saucers, but there is no textual support for that argument.
Change your thesis if you must. Sometimes a writer starts with one thesis, but finds herself arguing something else. Rather than make the paper conform to your thesis, adjust the thesis instead.