Writing a critical essay, to some degree, is the most difficult undergraduate composition task a student is likely to face. Critical thinking, after all, is the whole goal of higher education, and the critical essay calls on students to demonstrate an ability to use all the critical tools available to them within their field of study. Briefly defined, the critical essay may be considered any writing that utilizes the intellectual tools of a particular academic major for the purpose of critiquing another idea or point of view.
The operative word, then, for the critical essay is "critique." It's important, therefore, not to think of the critical essay as a negative analysis that sets out to prove something or someone right or wrong, which is the primary role of an argumentative essay. Sometimes, the critical essay is simply an intellectual appreciation of a given topic, object, or idea. In a literature essay, for example, a writer might use the critical tools available to an English major to write a critical essay that says: "This poem is good because it contains irony, which is critical to effective poetry." By using and defining the term "irony," the writer would show that he or she has a grasp of the critical language within the field of literature. Similarly, a scientific writer might use the basic critical tool available to science (the scientific method) to show that a certain study is either valid or invalid.
The key to writing a good critical essay, then, is understanding and defining the standard against which the object under study is being compared. For example, I may wish to show that a certain movie is good or bad. In order to do this, I need to define the elements of a good movie. These elements then become the critical standard by which my essay reviews and judges the film. A music critic, to use another example, does not necessarily say something bad about every CD released. Whether your critical essay is focusing on the negative or positive elements of a certain topic or thing, a good deal of the planning process should be devoted to comprehending and explaining the critical standard - or basis of critique - at the heart of your essay.