Identify any requirements for the paper that are specific to the form of the essay. For instance, a personal essay may not need a thesis statement, but an argumentative essay will. Be sure you are familiar with these special requirements regarding the form before you move forward.
Examine the content of the paper for adequate development of the specific topic. Are all main points discussed at adequate length? Did you find yourself feeling satisfied with explanations or were you wanting to know more information? Is the focus clear and appropriate for the paper's length requirement? Offer constructive criticism regarding elaboration or focus if you notice that some aspects of content development do not seem thorough enough.
Determine whether the style of the essay is appropriate to the topic. See if the tone fits the subject matter, if the language is at the appropriate level of professionalism (more casual for a narrative essay, more scholarly for a research paper, for instance), and if the writing is varied and sophisticated enough (avoiding too many short, choppy sentences, for example). Give concrete suggestions where you feel the style could improve.
Focus on the organization of the paper and whether it flows smoothly. Are the transitions appropriate and logical? Also consider whether the information is logically ordered and developed. Check for a solid frame of the introduction and conclusion and determine if they refer to the same ideas. If a thesis is required, evaluate whether it is clear, well developed, and not simply stating an obvious or well-known fact. If you find points where you feel confused or the organization is lacking, mark them and add suggestions for improvement.
Check the essay for correctness in grammar and sentence structure. Use a grammar handbook if necessary to help determine whether punctuation or syntax is correct. Mark the errors you find and suggest a correction for each.