For literature, how do you write a critical analysis?
A literary critical analysis includes a discussion of structure, thesis, language particulars and diction, plot and conflict, characters, and other literary devices of the literary element and literary technique categories, including mood and tone, tropes and conventions. In order to amass this information, you need to pay close attention to the elements and techniques, points and objectives in the writing as you come across them, paying special attention to subtle (or bold) changes in tone and mood as well as to words, phrases, or sentences that make, prove, or emphasize the author's thesis (major point).
To write your critical analysis, after your Introduction, you'll have a brief description or perhaps summary of the work you're analyzing followed a discussion of structural points. If you're analyzing a poem, this would include things like rhyme scheme, stanza construction, genre, and meter. If a book, this would include things like narrator, point of view, chronological orientation, overall mood (mood can change), and overall tone (tone can change). You then discuss literary elements and techniques, authorial style, the treatment of the work's thesis, and the work's effectiveness as these are relevant to your particular thesis statement--the point you wish to make about the literary work.
This may seem like a lot--and it can be--but it can also be abbreviated to suit the needs of your essay. For example, if my thesis is that a work is not effective because of faulty language, I may address structural elements as briefly as follows if I wish--if it serves my purpose to do so: The first person narrator establishes a despondent tone that matches the gloomy mood (same as atmosphere) as s/he paces back and forth in time between flashbacks, present day events, and anticipated future events while telling of the tragedy s/he witnessed on the slow boat to China two decades earlier.
I'm assuming that since your question is posted in the literature group that you mean a critical literary analysis. You can approach a critical analysis in several ways, but the main idea is to examine an idea or a theme or a symbol, or something that you see in a text that causes you to make some sort of evaluation. Then you use your text as a primary source to expand upon your idea, often supplementing that idea with outside sources - research, that is. Say, for instance, that you are studying the Shakespeare play Twelfth Night. Like any piece of narrative, even though it is a drama, the play contains a plot, characters, setting, themes, symbols, point of view, and literary devices. So, you might want to look at the theme of cross-dressing in the play, because Viola, the main character, has to disguise herself as a boy to survive.
Now you can take your idea and do a critical analysis from one of several different methods. You can do what is called "reader response," one of the easiest and most common (again, I don't know what your assignment is). That is to use quotes from the text to demonstrate what you think the author meant. Your quotes give validity to your ideas.
You can also do an analysis from a historical perspective, looking at how the issue you notice is based in the context of the time and how we would look at it today. The complexity of your analysis is going to depend on what your teacher requires of you and the level of understanding you bring to the text, so a high-school student would not be expected to do as complicated an analysis as would a college student.
I hope this helps.