Read the work thoroughly. If any questions arise as you read it the first time, reread it with your questions in mind until you find something compelling around which you can build an essay. You should consider the author's purpose and point of view. Keep an eye out for symbolism and allusions.
Pick a theme to examine and explore. It can be a topic that runs through the work as a whole, or something specific to a chapter or passage. You can look at elements related to the characters, the plot or even the structure of the book or poem you're analyzing.
Find evidence and examples of your theme. For example, if you were analyzing how "Hamlet" treats the issue of suicide, you'd want to discuss Hamlet's "To Be or Not to Be" soliloquy and Ophelia's death.
Write an introduction that outlines the subject you will analyze in the essay. Include a thesis statement that gives your take on the topic: for example, how you believe the literary work addresses a particular theme, or how important it is to the work as a whole.
Frame the body of your essay around the most compelling examples and evidence from the text. Support your analysis with these examples and provide context for your ideas.
Conclude by summarizing your points and restate your thesis in a new way. You can add another layer of insight related to your thesis, but don't introduce anything radically different at the end.