A critical essay combines a text (whether literary or otherwise academic) and your analysis of that text with expert opinion and contextual background. The aim of the critical essay is to analyze a work for (1) theme, (2) structure, (3) content, (4) purpose, (5) diction and rhetorical techniques, and (6) an evaluation of the worth, usefulness, goodness, etc of the text. In other words, a critical essay will analyze the parts based on textual proofs and evaluate the whole based on an external standard or a personal standard; in academia an external standard may be required.
Whatever the standard used for the evaluation element of the essay, you must always be "open-minded, well informed, and fair," as Elisabetta LeJeune of Southeastern Louisiana University pits it. Background information consisting of critical expert opinion and contextual information helps you achieve an open-minded, well informed and fair perspective. Your critical essay requires research (1) to ascertain what has been said before by experts in the field; (2) to set the work in contextual perspective (perhaps you are critiquing a philosophy essay that is itself a response to a previous essay); and (3) to uncover historical context (for example, historical context defines Frederick Douglas's work),
Background information is presented after your Introduction (which in British systems is no more than 5 percent of your paper but in the US system may be as long as you want it to be), which is where you introduce your topic, aim, purpose and thesis argument or question, After your Introduction you will develop the critical and contextual information your find pertinent. Background is important as the set-up for your own analysis that follows in the next section.
In your analysis, you will go into detail on the points enumerated in the first paragraph above. A very brief summary of the text will orient your reader to the essential content of the work under discussion. This summary will provide an opening for your discussion of structure and theme. The textual support you provide (textual support is critical for each analytical opinion stated) for these points will open the way for discussion of your analysis of the author's stylistics seen in diction and rhetorical technique. These considerations open the way to discussing the author's purpose and, from purpose, you will easily move into your evaluation of the work. Your evaluation forms the next section of your essay.
All that remains after your evaluation is to provide a Conclusion, which should be about the same length as your Introduction and which carries more weight than is commonly thought. Your Conclusion, though perhaps brief, is the place for you to raise criticisms of previous scholarship and to express insight into what further study is merited. These two components complement the reiteration of your analytical points to show how you have proven your thesis statement or answered your question.