The first step in critiquing an essay is to consider the overall content of the paper. Read the essay once or twice. Consider whether any of the content in the essay doesn't seem appropriate or necessary to the theme or argument presented in the essay. Make notes where anything is unclear or seems out of place. The content of the essay should be concise and clear without any missing elements, facts or important information. You should be able to read the essay and have it make sense whether or not you are well-versed in the subject matter.
The second step to critique an essay is to consider the overall voice and style of the paper. Whether it's written in the first or third person, the essay should convey an authoritative voice. Consider whether the tone of the essay is informational, humorous, or argumentative. The tone should stay consistent throughout the essay. A good way to critique the voice and style of the paper is to read it aloud. Ask yourself whether or not it flows in a way that is appropriate for the subject matter and the academic guidelines for the essay. Give the writer a summary of how the voice and style either work or don't work.
The next step is to go over the essay and consider how it is organized. In most cases, there should be an introductory section, a clear thesis, supporting content or facts, and a conclusion. Regardless of the type of essay - argumentative, personal, reflective - it should be organized in a way that best covers the topic. Subtopics should be placed under appropriate categories. Supporting information should clearly support the thesis, and information should be presented in a logical order. If the organization needs to be changed, make notes where you think sections should be moved or rearranged.
The final step in critiquing an essay is to proofread it for grammar, spelling, punctuation and style errors. If citations are used, they should be properly attributed according to the style used such as MLA or APA. Check for common errors like subject-verb agreement and missing or misplaced commas. Also look for mistakes in spacing, margins or information on the Works Cited page. Make corrections using standard proofreading marks or whatever style you use when editing.