Read and re-read the short story. Use these times of reading to make notes and to determine what you feel is the meaning of the work --- what the writer is attempting to convey. These will be the foundational points of your analysis.
Seek out theme, character, setting, plot, tone, point of view and conflict within the story. These elements help reveal to you the meaning behind the story. Consider the elements of fiction to be a facade to cover up a moral or point of the story.
Outline your paper. Use a standard essay outline for your paper, but give yourself room within the body characters to flesh out quotes and background from the story coupled with your own opinions on the meaning.
Write your paper. Write first your thesis statement, then your body paragraphs and conclusion. Following these, write your introduction. It is often easier to write your introduction after you have already made the main points and concluded your thoughts. Include your thesis statement in your introduction.