In Rhetoric, written by Aristotle in 350 BCE, Aristotle explains the three attributes of effective persuasion.
Of the modes of persuasion furnished by the spoken word there are three kinds. The first kind depends on the personal character of the speaker [ethos]; the second on putting the audience into a certain [emotional] frame of mind [pathos]; the third on the proof, or apparent proof, provided by the words of the speech itself [logos]. (Book 1, part 2)
Aristotle then perfectly describes Iago's rhetorical skills as demonstrated in Shakespeare's Othello.
There are, then, these three means of effecting persuasion. The man who is to be in command of them must, it is clear, be able (1) to reason logically, (2) to understand human character and goodness in their various forms, and (3) to understand the emotions, that is ... to know their causes...
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and the way in which they are excited. (Book 1, part 2)
Aristotle believes that a person's credibility and character are the most important aspects of persuasion.
Persuasion is achieved by the speaker's personal character when the speech is so spoken as to make us think him credible. ... his character may almost be called the most effective means of persuasion he possesses. (Book 1, part 2)
Iago knows that Othello has a trusting nature:
IAGO. The Moor is of a free and open nature,
That thinks men honest that but seem to be so;
And will as tenderly be led by the nose. (1.3.409-411)
Iago also knows that Othello trusts him implicitly. Othello repeatedly refers to him as "honest Iago" in his conversations with Iago and with other characters.
OTHELLO. (to the Duke of Venice) So please your Grace, my ancient;
A man he is of honesty and trust. (1.3.302-303)
The person who Iago uses to effect his revenge against Othello thinks him honest.
CASSIO: Good night, honest Iago. (2.2.321)
Even Desdemona is convinced of Iago's honesty, and she appeals to Iago to help her win back Othello's love after Othello turns against her.
DESDEMONA. O good Iago,
What shall I do to win my lord again?
Good friend, go to him ... (4.2.168-170)
All of this trust and his own seeming honesty works to Iago's advantage.
Iago is well aware that he needs his victims' trust (ethos), and he's also aware that he can appeal to them through their emotions (pathos). He convinces Brabantio that Othello has bewitched Desdemona. He convinces Roderigo that he can win Desdemona away from Othello. He convinces Cassio that he's his friend and confidant, and uses Cassio's love for Desdemona to manipulate him.
Iago is also well aware of Othello's emotional weaknesses—particularly his propensity towards jealousy—and early in the play, Othello tells Iago exactly how to persuade him that Desdemona is unfaithful to him.
OTHELLO. ... 'Tis not to make me jealous
To say my wife is fair, feeds well, loves company,
Is free of speech, sings, plays, and dances well;
Where virtue is, these are more virtuous.
Nor from mine own weak merits will I draw
The smallest fear or doubt of her revolt;
For she had eyes and chose me.
No, Iago, I'll see before I doubt; when I doubt, prove;
And on the proof, there is no more but this,
Away at once with love or jealousy! (3.1.206-215)
Iago follows Othello's advice and uses the evidence of Othello's own eyes and ears (logos) to destroy Othello and Desdemona.