How does Iago control what happens in the play Othello?
Iago doesn't so much control what happens in the play as he manipulates the other characters so that events happen the way that he wishes. The three characters most affected by his psychological warfare are: Roderigo, Cassio, and Othello.
Iago exploits Roderigo's love of Desdemona to great effect. He convinces Roderigo to be his front man, taking the fall for his inflammatory words and announcing to Brabantio that his daughter Desdemona has eloped with Othello. He also convinces Roderigo that if he would simple "put money in [his] purse" he (Iago) could secure him Desdemona's love. Iago intends to put Roderigo's purse to his own use.
Next, Iago exploits Cassio's drinking problem. Today, we would say that Cassio is an alcoholic, and as such doesn't have much control over his behaviour when he drinks too much. Iago fills him up with alcohol, which leads to Cassio being involved in a barroom brawl, which leads to Othello stripping him of his position. This demotion is the cause for Desdemona to spend most of her stage time pleading for Cassio's reinstatement, which adds fuel to Othello's jealous fire.
But Iago's most masterful manipulation is the stirring of Othello's jealousy. He is most skillful here, seeming to have Othello's best interests at heart, seeming to be cautioning Othello against the thing that he is, in fact, encouraging -- the belief that Desdemona and Cassio are having an affair. Othello, of course, is inflamed to such a degree that he causes his own demise by murdering his wife in their bed.
The genius (albeit evil genius) of Iago is that he doesn't actually cause any of the disastrous events, he is simply able to manipulate others to do the dirty work.
Iago is the puppeteer; the other characters are his puppets. He pulls the strings; the other characters dance to his music. He enrages Brabantio with his coarse language about Desdemona's elopement to Othello. He manipulates Roderigo, getting him to sell all his lands: "thus do I ever make my fool my purse." He convinces Roderigo that he can have Desdemona if he will give Iago more money to gain her affections. He uses peer pressure to get Cassio who has "poor and unhappy brains for drinking" to get so drunk that he injures Montano. He persuades Cassio to go to Desdemona to regain his position as lieutenant. And last, but most importantly, he convinces Othello that Desdemona is cheating on him and leads him to the conclusion that she and Cassio must be executed.
That said, Iago's powers are limited, and the characters allow themselves to be pawns. Iago appeals to their dark sides; the characters have responsibility for their fates. Brabantio might have trusted his daughter's judgment and respected her choice of a husband. Roderigo, if he truly loved Desdemona, would not have interfered in her marriage. Cassio knew he was not capable of holding his liquor and should not have allowed himself to drink, while he was on duty. Othello, of course, should have trusted his wife.
Iago's machinations throughout the play are masterful. Even Othello cries out at the end of the play, wondering why this "demi-devil... hath ensnared my soul and body." Yet, the characters are not complete victims of his design. They make choices that ultimately lead to tragedy.
Iago uses words to control what happens in Othello. He has a great ability to understand the feelings and desires of the people around him. With that understanding he wins their trust while instilling in them distrust towards others. Finally manipulating them through persistent persuasion to do what he wants.
Iago is a master manipulator of people and he gets the other characters in the play to do just what he wants. he manipulates others through a keen understanding he seems to have of what motivates them.