How does a persuasive writer establish ethos with the reader?
The term "ethos" comes from the classical Greek rhetorical tradition. It is linked to our modern English word "ethics," but it also implies a wider range of qualities: character, position in a community, and personal authority. Therefore, a persuasive writer establishes ethos in his or her work through showing or demonstrating each of these things.
To write ethically, one does not plagiarize. One also gives full credit to all sides of an argument, including those arguments with which one disagrees.
To show character, one is fair and inclusive.
To show position in a community, one includes references to shared values and shared sources of authority (a Christian might quote the Bible, for example), but also by using shared language patterns.
To show personal authority, one includes references to experience or credentials that apply. A major league baseball player might mention playing in the World Series, for example.
In short, in relation to 1984, one does the opposite of Newspeak.
It is best to start with a working definition of ethos to answer this question. Fundamentally, ethos is "the distinguishing character, beliefs or moral nature of a person, group, or institution." According to Aristotle, the chief components of a compelling ethos are good will, practical wisdom, and virtue.
Orwell establishes ethos in his novel "1984" in a negative way. Essentially, none of the characters portray positive ethos. Even the alleged protagonist, Winston Smith, is fundamentally lacking in Aristotellian terms. True, he treasures his individuality, but his motiviations are hardly altrusitic. Instead of selflessness and good will, Smith instead is motivated by personal motivations, chiefly sexual and intellectual in nature.