To begin, one needs to be sure to understand what the idea of ethos is. Ethos is, in very simplistic terms, the appeal of the author (based upon the author's reputation). Therefore, an author develops his or her pathos through the way they address the audience, their tone, and the subject matter of the text.
In regards to Robert Rodriguez's Aria: A Memoir of a Bilingual Childhood, Rodriguez is able to establish his pathos by beginning his essay speaking about his difficulty in schools in America (given he could "only understand about fifty stray English words").
Rodriguez goes on, in the second paragraph, to state that he was surrounded by the white children of doctors and lawyers. Given he recognized, immediately, that he stood out, Rodriguez knew he was destined to be "the problem student in class." In paragraph three, Rodriguez recalls the first time he heard his name spoken in English: "Rich-herd Road-ree-guess."
Therefore, Rodriguez establishes his ethos by describing a place in his life where readers can either relate or wish to know about. People reading his text most likely are studying the problems associated with learning a second language or with the feelings associated with learning another language. Regardless, a reader knows that Rodriguez has lived a life as a second-language learner. His knowledge about the subject can be seen as reliable and his ethos is both understandable and trustworthy.