Caliban, Stephano, and Trinculo continue to get drunk. Stephano who now calls himself "Lord of the Island," commands Caliban to "Drink, servant monster, when I bid thee" (3.2.7). Stephano declares that Caliban will be his lieutenant. When Trinculo, who is baffled by Caliban's worship of Stephano, mocks Caliban, Stephano threatens to have Trinculo hanged.
Stephano is drunk on power. Commanding Caliban, dispensing favors and rank, and threatening to have people hanged. It's funny because it's so dumb, but it's also a critique of those who seek power for selfish reasons, such as Antonio.
Ariel, invisible, enters just as Caliban begins to describe Prospero's ill treatment of him and to ask Stephano to avenge this wrong. Ariel calls out "Thou liest." But because he is invisible, the Caliban and Stephano thinks that it is Trinculo who has spoken. Stephano threatens Trinculo, who denies having said anything. When Arial again shouts out "Thou liest," Stephano punches Trinculo.
This is another comical scene. It highlights the ways that Prospero uses magic to control and manipulate the other people on the island.
Caliban continues to describe his plan to murder Prospero. He suggests several ways of killing Prospero, and it is clear that he has thought about this before: "Thou mayst brain him ... or with a log batter his skull, or paunch him with a stake, or cut his wezand with they knife" (3.2.80-83). But it is vital, he says, for Stephano to seize Prospero's books, which are the source of his power. He entices Stephano by promising Miranda as a prize once the deed is done. Ariel listens in and makes plans to tell Prospero of the plot.
Caliban seems to revel in the thought of Prospero's destruction. He knows that Prospero's books are the source of his power, so Caliban demands that Stephano seize the books but not destroy them. The implication is that Caliban might appropriate them and use their power when Prospero is gone.
The three men begin to sing loudly in celebration but cannot recall the tune they want to sing. Ariel supplies it, throwing Stephano and Trinculo into a fright. Caliban reassures them, delivering a lyrical speech about the island's many curious and entrancing sounds. He says, "The island is full of noises, sounds, and sweet airs, that give delight and hurt not" (3.2.127–128).
Stephano exults that he will soon be the lord of such a wonderful island "where I shall have my music for nothing" (3.2.139–140). Ariel exits, still playing music, and the three men follow the bewitching sound.
Caliban loves the island, while Stephano wants to rule the island. In contrast to Stephano, Caliban seems to have some similarities to the Noble Savages described by Gonzalo in Act 2, scene 1.