How do you rhetorically analyze somebody's essay? What are the elements to look for? The essay under evaluation is controversial claim by a...

The previous thoughts are well asserted.  The content is
not as important as how it is stated or phrased in a rhetorical analysis.  Prior to
this, I would ask if a rubric is present.  In many of these situations, there is a
rubric that outlines what is being assessed and how it is being evaluated.  If you or
your instructor has one, then I would ask to see if this could be used as a reference
point.  All essays are much easier to grade and more clear in the assessment analysis
with a rubric, as opposed to wide ranging thought and input that is not consistent with
stated goals or expectations.  If you are able to do so, there are many examples of
rubrics available on line for free that you can download or modify to your own
standards, or those of your instructor.  If these can be accessed and used, I would
strongly suggest doing so.  In terms of general basics on rhetorical analysis, I would
pay attention to how the paper has used word choice, syntax, and persuasive elements to
convince the reader of its thesis.  Simply put, how has the argument been framed through
language?  This is where a rubric would be extremely helpful.