Iago's persuasive ability comes from trickery and believable lies. Othello's persuasive ability comes from his power and his position as General. Desdemona's ability comes from her innocence and beauty.
Throughout the play, Iago uses little tricks to gain the trust of Othello and eventually persuade him towards his side. He is very subtle at first, only hinting that Desdemona is cheating on Othello. However, as the play progresses, he gets more and more specific by blaming it on Cassio, pointing out the missing handkerchief, and finally telling Othello how to kill her. Iago's speech is very subtle in the art of persuasion and yet it works almost perfectly.
His way of persuading someone towards his view is by letting the person, Othello in this case, fill in the obvious blanks. He does this by simply hinting at the certain thing Iago wants him to see. When Iago is confronting Othello to his face and trying to convince him he brings up many points but one of the most disturbing to Othello is when Iago mentions his handkerchief. Iago says, “I know but that; but such a handkerchief - I am sure it was your wife's - did I today see Cassio wipe his beard with.” (149) He doesn't even say straight up that Desdemona gave her handkerchief, just lets Othello assume that's the only way Cassio could have gotten it. Of course, Othello falls right into Iago's trickery again.