Look for recurring words, images, phrases or situations. Often these repeated elements, called "motifs," signal important themes or symbols in the story. For example, in Ayn Rand's "Atlas Shrugged," the question "Who is John Galt?" occurs repeatedly at key moments and comes to represent both the apathy of most of society and the willingness of exceptional people to rise above it.
Think about what the author associates with each motif or symbol to develop ideas about what it represents. Some items have commonly recognized symbolic value, such as a dove representing peace. Authors may also subtly interpret their own symbols by connecting them with related events, questions, choices or facts. For example, a locket a character's mother gives her may come to represent the mother, especially if the character's emotions about the locket are similar to those about her mother.
Follow the characters' important choices and dilemmas to get an indication of the major thematic questions in the story. Often different characters (or one character at different times) will respond to related dilemmas in different ways. For example, if one character abandons monastic life to seek wine and women while another character turns down an attractive marriage proposal to care for her dying father, a driving thematic question may be "Does discipline or passion lead to a happier life?"
Watch the consequences of the characters' actions to find the author's solution to or perspective on the theme questions. For example, if the character who stays to care for her father finds fulfillment through her sacrifices, the story may be communicating that discipline is ultimately rewarding. If, on the other hand, she ends up a bitter and regretful old maid, the theme of the story may be that grasping immediate pleasures is the only reliable way to have a full life.
Re-read the story (or scenes that stood out to you) in light of the themes you found. Often symbols and choices will take on new significance once you know where the story is going.