In addition to the answers above, Iago is a compulsive liar and is extremely convincing in his speech. He uses his tone of voice and facial expressions (in movie and theater versions) to appear believable and carefully chooses his words (this is called "diction) to be able to manipulate Othello, Cassio, Roderigo, etc. Iago is a master orator and uses this to his advantage.
Iago exploits strength and weakness alike. As Shakespeare often points out, at times it is difficult to see the line dividing the two. Roderigo loves too much; Iago exploits his obsession. Cassio needs his reputation; Iago finds his weakness (drink) and uses it to destroy him. Emelia, for all her talk, seems to want to be on his good side. He uses her desire to please, getting her to steal the handkerchief that Desdemona drops. Desdemona is kind. In this is the cruelest manipulation of all. He counts on her kindness and reinvents her motive. Iago is brilliant in that he uses whatever people are already inclined to do for his benefit. It is barely a manipulation, yet his control is complete.
Great Question. Iago has perfected the art of manipulation. In Othello. Although the play is named for one of the characters, many scholars argue that Iago is actually the protagonist. Much of the focus of the play is on Iago's relationships with the other characters.
One of the characters he manipulates often is Roderigo. From the very opening scene we see Iago manipulating Roderigo. Iago uses Roderigo's obsessive love for Desdemona to convince him to do things that are not very nice. For example, in the first scene Iago and Roderigo snitch on Othello and Desdemona. They have eloped, and Iago convinces Roderigo to wake Brabantio, Desdemona's father, and anger him with the news that, "An old black ram is tupping your white ewe." In Shakesperian language, that's not a pretty picture.
Toward the end of Act II, scene iii we see Iago manipulating Cassio. Cassio has just been fired from the position of lieutenant due to a brawl with a prominent Cyprian (that Iago set up, by the way). Iago advises Cassio to go to Desdemona for help. He insists that if Cassio curries favor with her, she can help him convince Othello to give him back his job. Iago is really trying to get Cassio close to Desdemona, however, so he can begin to convince Othello that they are having an affair.
This play is full of scenes of Iago controlling other characters through manipulation. In fact, the plot of this drama is completely dependent on it.