In act 1, scene 3 of William Shakespeare's Othello, Iago's initial plan is to have Brabantio, Desdemona's father, denounce and disgrace Othello in front of the Duke and his council of Senators for eloping with Desdemona.
Desdemona's marriage to Othello is upheld by the Duke and the council, partly for political reasons—they need Othello to defend Cyprus from the invading Turks—and partly because of Othello's skill in convincing the Duke and the Senators that his motives and methods in winning Desdemona as his wife were entirely honest, and that he truly loves her.
Iago's plan has failed, but Iago seems to be not the least dismayed or deterred by this turn of events. He simply hatches a new plan to try to destroy Othello.
It's in this scene, after Brabantio reluctantly makes a show of his blessing of Othello and Desdemona's marriage, that Brabantio unknowingly plants a seed in Othello's mind that Iago will nurture and cause to grow into a jealous rage that will ultimately destroy Othello, Desdemona, and Iago himself.
BRABANTIO. Look to her, Moor, if thou hast eyes to see;
She has deceived her father, and may thee (1.3.313–314).
With these lines and this thought in mind, Iago decides to insinuate to Othello—who will "as tenderly be led by the nose / As asses are" (1.3.411-412)—that Desdemona is being unfaithful to Othello with Cassio, who Othello made his lieutenant instead of Iago and against whom Iago now holds a grudge.
IAGO. Cassio's a proper man. Let me see now:
To get his place, and to plume up my will
In double knavery—How, how? —Let's see—
After some time, to abuse Othello's ear
That he is too familiar with his wife (1.3.402–406).
Iago also suspects that "the lusty Moor / Hath leap'd into my seat," meaning that his wife, Emilia, might be unfaithful to him with Othello.
By suggesting to Othello that Cassio and Desdemona are having an affair right under Othello's nose, Iago can get revenge against Cassio and Othello.
Regarding Desdemona, the unwitting pawn in Iago's scheme, Iago confides in the next scene, "I do love her, too" (2.1.299), but he loves her only insofar as he can use her to destroy Cassio and Othello.