At the end of Act I, Scene 1, Iago tells Rodrigo that, while he hates Othello, he must join him. In part, Iago is angry because Othello appointed another man as his lieutenant, and Iago plans to pretend to be faithful to Othello, but in reality will be like other servants who feign obedience to their masters but "keep yet their hearts attending on themselves" (Act I, Scene 1, line 54). In other words, he plans to pretend to be loyal while thinking about himself and his own advancement.
At the end of the scene, after he and Rodrigo wake up Desdemona's father, Brabantio, and tell him Desdemona fled to go to Othello, Iago tells Rodrigo he must return to Othello. Iago knows the government of Venice might scold Othello for stealing away with Desdemona, but the government needs Othello for their war against Cyprus because he is so talented at leading men in war. While Iago hates Othello, he will pretend to be loyal. He tells Rodrigo that Othello is likely to be at the Sagittary Inn. This way, Rodrigo will lead Brabantio to Othello, while Iago will still appear to be a faithful servant to Othello.
Having confessed and explained his hatred of Othello to Roderigo, Iago secured the help of Roderigo in his first stratagem against Othello. They go to the house of Brabantio where they awake the household with the news that Desdemona, Brabantio's beautiful daughter, has eloped with Othello. Having roused the household successfully, Iago decides to leave Roderigo before he has to face Othello, saying that although he desires to hurt and damage Othello, he is too popular at the moment to oppose openly:
Though I do hate him as I do hell-pains,
Yet for necessity of present life
I must show out a flag and sign of love
Which is indeed but a sign.
Having employed Roderigo to his dirty work for him, Iago therefore goes to be with Othello so he can appear innocent of the attack that he has unleashed on his master.