Thanks for your question. The very first thing you must do is follow the instructor/professor's instructions. You will often find that teachers/professors have a specific format you must follow. For example, are you asked to compare the life of Hemingway to themes in "Hills Like White Elephants?"
If so, proceed by identifying major themes of Hemingway's life story, such as his disillusioned response to World War I. This could be compared the seemingly nonchalant reaction of the American man to Jig's condition in the story. Hemingway is also known for creating male characters with a very fixed sense of masculinity; the American in the story is representative of this--especially the way he talks about the 'operation' he feels Jig should have.
If you are not charged with comparing his life to the story, then I would proceed this way. Open the essay with context and background about Hemingway's life. Then, provide a brief summary of the story, followed by your claim about the story. Your claim (thesis) might be that the white elephants (a symbol of something everyone knows is there but no one wants) is representative of the assumed pregnancy as well as the relationship between the two characters.
Follow this with a body paragraph about the assumed pregnancy being a white elephant, try to quote from the text; use the American's explanation of the operation and how he feels it will solve their "problem."
Write another body paragraph about Jig and how she probably knows the relationship is not one she wants anymore. Cite the way she no longer thinks the hills look like white elephants; this may signal a shift in how she feels about her pregnancy and the man she is with.
You can conclude with a brief summary of your argument and a conclusion that says this story is not unlike others of Hemingway's with similar themes.