Othello tells Cassio to keep the party under control. Cassio notes that actually that's Iago's job, but sure, he's willing to help out. After Othello says he trusts Iago (bad move), he tells Desdemona he's paid for her by marrying her, and now it's about time that he gets to collect.
Once Othello leaves, Iago meets with Cassio, all ready to start their night-watch together (they're guarding the court while everyone else gets their party on). Iago notes its actually only 10pm, way too early to start. Obviously, Othello only put them on watch because he had some business to attend to.
Iago then prods Cassio to talk about how appealing Desdemona is. He tries to get Cassio to call the girl a whore, but Cassio's more of a gentleman than that. When it doesn't work, Iago tries to convince him to drink.
He prods Cassio, saying they've got friends coming that would be happy to have a drink in honor of "black Othello." Cassio points out that he's kind of a lightweight, and he's already had his one drink for the night.
Iago turns the peer pressure on full blast, and Cassio finally consents to invite the friends in for a drink, even though he doesn't feel good about it. Left alone, Iago reveals his master plan of drunkenness: he hopes to get Cassio hammered, knowing that Roderigo's been drinking all night in the name of his lost love. Once the three drunk Cypriots, who are quick to fight when saucy, are tossed in the mix, a rough and tumble night is guaranteed.
As the young gentlemen of Cyprus (the gallants) enter with Montano and Cassio, Cassio declares they've already given him another drink. Iago, thrilled to bits, sings a drinking song and calls the Danish and Dutch people poor comparisons to a British drunk.
Iago then sings another song, of a King Stephen who's too distracted by his clothes, and so loses his kingdom. (This is handy if you're reading The Tempest, as Shakespeare alludes to this song again when would-be king Stephano gets distracted by a wardrobe and so sacrifices his dominion over the island.)
The point is, everyone's getting sauced. Cassio, lightweight that he is, gets drunker than everybody else, and begins to moralize about how they shouldn't be drunk, as he'd like his soul to be saved when he dies.
Iago agrees that he, too, would like his soul saved, but Cassio says Iago should wait to die after him, as lieutenants should have their souls saved before dinky low-ranking flag-boys. Cassio continues undiplomatically that they should all look to their business as though they weren't drunk.
He insists that he's not drunk, and he's so not drunk he can even distinguish his right hand from his left hand. Definitely not drunk.
Cassio then heads off with the other drunken men to start their night watch, leaving Montano, Governor of Cyprus, alone with Iago. Not shockingly, Iago does his usual thing when left alone with someone: he slanders the person who's just left the room.
Iago says that Cassio's virtues are well balanced with his vices, suggesting the lieutenant is extreme in both his good and bad behavior. Iago adds that Cassio drinks himself to sleep when he can. Montano, hearing this, concludes that Othello is too good-natured to recognize Cassio's alcoholism.
Roderigo then enters, and Iago sends him off after Cassio. This is a setup for a fight between the two. Iago continues to shoot the breeze with Montano when Roderigo runs in—chased by Cassio. As Cassio hits Roderigo (who literally asked for it), Montano tries to stop him. Naturally, Cassio turns his drunken fury on Montano.
Iago instructs Roderigo to run and make a ruckus about the fact that a mutiny has started, and then acts all surprised when, shortly after, the town bell is rung (likely by Roderigo). This makes it a sure bet that Othello will come in and ask just what all the fuss is about.
Then… Othello comes in and asks just what all the fuss is about. Iago feigns innocence and says he doesn't know how the brawl started, he just saw everyone fighting like they were suddenly transported to a schoolyard.
Othello demands explanations: Cassio says he can't speak, and Montano, claiming to be weak from blood-loss, says he's only guilty if he can be blamed for not being able to protect himself.
So Cassio's drunk, Montano's claiming self-defense, and Othello's mad. He says his passion is beginning to overtake his reason, and everyone's going to get a beating unless this gets cleared up immediately. Further, it's for shame that the men make such a ruckus when the poor people of Cyprus feel like they're at war, and their supposed rescuers can't even manage their own domestic disputes.
Othello calls on Iago to explain, who claims he would never speak a bad word against Cassio. He says he was chatting with Montano when a fellow ran in crying for help, with Cassio in hot pursuit. Montano, stepping toward Cassio to calm him down, got pulled into the fray.
Iago continues: he chased after the yelling fellow to stop him from waking the city (mission not accomplished), and Cassio and Montano were embroiled in a fight by the time he came back. (All in all, Iago claims he wants to protect Cassio, but in actuality, he deliberately makes Cassio seem to be the one at fault.) Othello thinks Iago's meager report of Cassio's wrong is his attempt to cover for Cassio, which lets him imagine that Cassio is even more at fault. Mission accomplished.
Furious, Othello fires Cassio from his position as one of his officers. Desdemona comes in, confused. Othello tells her to go back to bed, but says in the meantime that he has to take care of the wounded Montano.
After they leave, Iago pretends to make nice with Cassio, asking if he's okay. Cassio replies that he's mortally wounded, and Iago gasps, but it's not a physical injury that's bothering Cassio.
Cassio says in this fight, his reputation has suffered irreparable harm. Iago comforts him, stating that reputation is a stupid marker by which to judge people, as it's earned and lost so easily. Iago claims Cassio has no reputation at all, "unless you repute yourself such a loser."
Anyway, Iago insists that Cassio can win back Othello's affections, as Othello punished Cassio more because it was immediately necessary than out of any long term hate.
Iago asks if Cassio remembers why he chased that one guy (Roderigo), and Cassio says he remembers a lot of stuff, but not any particular offense. He goes on to blame wine for a bit, and generally condemns drinking until Iago cuts this off.
Iago suggests that Cassio go to Desdemona and get her on his side. After all, she and Othello might as well share one mind. Desdemona is so nice, Iago claims, that she'll be eager to help Cassio, and certain to persuade Othello to take him back (as an officer). Cassio thinks this is a grand idea, and says he'll go to Desdemona in the morning.
Iago is then left alone. As usual, he informs us that he's very pleased with himself. Even if he were an honest guy who was Cassio's friend, he would have given him the same advice: go get help from Desdemona. It just so happens that this "good advice" plays right into Iago's plan to make Othello jealous of Cassio. Gleefully, Iago realizes that Desdemona's kindness to Cassio will be her downfall.
Roderigo comes in, fresh from the beating from Cassio, and says he thinks he should give up and go back to Venice, as now he's poor and bruised up. Iago tells him he has to be patient; though Cassio technically won the fight, the injury against Cassio will have longer effects. The fight's gotten him fired, after all, and who knows what it might bring upon him later.
Iago dismisses Roderigo and goes back to bad-guy scheming. First, he plans to get his wife (Emilia) to try to plead Cassio's case to Desdemona. Second, he will try to get Othello all to himself, and then conveniently lead him to someplace where he can chance upon Cassio in intimate private speech with Desdemona, in a classic "it's not what it looks like, honey" moment.