Read, watch or view the piece of work you are planning on writing about in your critique. Merriam Webster's defines a critique as "a critical estimate or discussion," so you will be evaluating the positive and negative qualities of a piece of work, usually artistic -- literature, painting, film and so on -- or intellectual nonfiction such as philosophy or sociology.
Make a list of the work's positive and negative qualities. This will help you define the scope of your argument, as well as provide some of the structure for your critique -- commonly, each point will become a paragraph or section.
Survey any other critical work discussing the work in question. This will help you understand how the work has been received, as well as provide arguments to support your thesis or opponents to argue against.
Formulate your preliminary thesis statement. A thesis statement, as the name implies, must be a firm statement. It cannot be a question; it must declare a distinct opinion.
The thesis statement will usually include several clauses. Make sure that it indicates the field and scope of the topic being discussed. You must also indicate the argumentative tack that you are taking, leaving the reader with a clear idea of where the essay is headed as well as your own position on the subject.
Write your essay with your thesis statement in mind. Write out your thesis statement on a Post-it and stick it to the side of your computer monitor, so that you can check back to it quickly and easily.
Refine your thesis statement as you write your critique. Pieces of writing change constantly through the writing and editing process, so you should revisit your thesis statement when you have a finished first draft and make sure that you have actually written the essay you planned on writing. If necessary, you should then revise the thesis statement to better fit the piece of writing you have produced.
Or, if you believe the thesis statement correctly encapsulated your intended argument, you should revise the essay again with the thesis statement in mind, making sure that each element of the statement has been properly covered in your essay.