Ethos, or the speaker's character, helps a speaker be persuasive by demonstrating expertise in a subject, as in the case of a scientist talking to laypeople. Arguments from logos -- reason or logic -- pertain to how a speaker reasons. Logos analysis examines whether the speaker uses inductive or deductive reasoning, whether his arguments are logically correct and whether his evidence supports the conclusions. Speakers also appeal to pathos -- emotion -- as when a charity evokes pity by showing pictures of starving children to persuade donors to give money.
Certain standard types of argument are know as the "common topics." These are not subjects, but approaches. They include such standard rhetorical strategies as definition, comparison and contrast, amplification and weighing of honor versus expediency. Identifying use of common topics is an important part of analyzing arguments.
Style can be "low" and include simple words, short sentences and minimal use of figures of speech. A high style includes ornate language and arguments, many figures and tropes, and elaborate sentence structure. Middle style defines ordinary academic writing, which should use elements of high style sparingly. Rhetorical analysis uses highly technical terminology to describes the figures of speech and thought which characterize a writer's style, including terms for types of sentence structure, patterns of sound and striking sentence-level ways of expressing thoughts.
Rhetorical analysis examines how speeches are structured. A speech may have a deductive structure, moving from a general point to specific implications, or an inductive structure, which piles up examples to lead to some general conclusion. Some works are organized chronologically, describing events in the order in which they occurred, while others compare and contrast different situations or ideas. Drawing an outline of the major arguments can be a good way to examine the structure of a speech or essay.
Crucial to a good rhetorical analysis paper are cover argument, arrangement and style. Be sure to show how each rhetorical device contributes to the overall effect of the work you are analyzing. Only summarize when it supports analysis, as excessive summary is considered a weakness in analytic papers.