Locate the writer's argument. Test whether the argument is debatable by taking an opposing stance to it. If the thesis is not arguable, it does not present an argument but a description or statement of fact. For example, the thesis "J. R. R. Tolkien writes about fantasy" merely describes Tolkien's writing. However, the claim "J. R. R. Tolkien peoples his fantasy world with characters that represent a strict dichotomy of good and evil" is a valid thesis because someone could argue the opposite view, that Tolkien's characters are not simply either all good or all evil.
Determine whether the argument expresses a personal preference. Personal preferences are not valid theses, because you cannot argue against them using evidence. For example, "J. R. R. Tolkien is a good writer" is too subjective a statement to debate.
Note any bias in the argument. Take into account whether the author's background might be influencing her argument or if her argument appears to have sprung from an objective consideration of evidence.
Decide if the argument can garner a sufficient amount of evidence, or if it is too narrow to find enough support. Likewise, if an argument makes too broad a claim it will struggle to organize too many ideas and fail to convince because it lacks specific evidence.
Write a three-to-five paragraph essay on the argument once you have evaluated it. Begin with an introductory paragraph that summarizes the argument and quickly previews your opinion of the argument.
Divide the body of your essay into either the strengths and weaknesses or two or three main aspects of the argument you want to address. Praise the argument's strengths and tactfully address its weaknesses.
Suggest areas of improvement in a concluding paragraph. Specifically explain ways the writer can clarify and solidify his argument, such as narrowing it, broadening it or inserting a stronger opinion into it.