During a tremendous storm, a ship carrying passengers from several Italian kingdoms runs aground. The action begins on board, as the titular tempest batters the vessel, and the passengers argue with the boatswain over the best course of action.

The passengers include Alonso, the king of Naples; his brother Sebastian; his son Ferdinand; and the king's loyal counselor, Gonzalo. There is also Antonio, the current Duke of Milan, who we later learn usurped the throne from his brother Prospero. As the ship is about to split, Antonio decides to abandon the king; the scene ends with the shipwreck imminent.

In the next scene, there is a conversation in which the spirit Ariel tells his master, Prospero, that he has carried out his orders. It is revealed that Prospero ordered Ariel to cause the storm. Ariel states that, while the mariners stayed aboard, the passengers jumped into the sea. Ariel then reveals that the ship is docked in the harbor, so the mariners are safe. He states that the royal party, on the other hand, has been scattered and washed ashore.

Ariel then sings songs to Ferdinand, claiming that his father has died, which leads him to the cave where Prospero lives with his daughter, Miranda. The young prince meets Miranda outside the cave, and it is love at first sight. It is revealed that it was Prospero's intention to lure Ferdinand (whom he wants Miranda to marry) to the island as part of his plot to win back his dukedom. Prospero then enchants Ferdinand to make him weaker and forces him to labor in a woodpile.

Meanwhile, Ariel's magic puts a sleeping spell on the other members of the royal party, but Antonio and Sebastian are left awake. While Alonso and Gonzalo sleep, the two noblemen conspire over the throne of Naples. They plan to kill Alonso and Gonzalo as they sleep, but when they pull their swords, Gonzalo and Alonso (again, through Ariel's magic) wake up just in time. When the would-be murderers pretend to have been protecting them, the king believes them.

The next character introduced is Caliban, an ill-tempered man whose mother was a sorceress. He has been enslaved by Prospero and curses him for it. Another character is Trinculo, the king's jester, who shelters from the rain beneath Caliban's cloak. Stephano, a buffoon who rode a barrel of wine ashore, is astonished to recognize his friend when he also takes shelter under the cloak. As the three men drink together, the intoxicated Caliban believes Stephano to be a god and decides to support him in overthrowing Prospero as the island's ruler. This creates a parallel plot to the other conspiracy, and they head off to kill Prospero.

Elsewhere, Prospero sets a trap for the noblemen by setting out a magically contrived banquet; however, when the men try to eat the food, the vision is replaced by Ariel in a terrifying form. In this state, Ariel castigates the royal party and informs them that the storm was a product of their misdeeds.

Concurrently, Prospero releases Ferdinand from his log-sorting task and tells him that he has passed this trial and thereby earned Miranda's hand. Caliban's plot threatens to spoil their celebrations, but Ariel successfully tempts the conspirators to steal Prospero's royal garb. When they take the garb, however, the thieves are repelled by spirits in the form of dogs.

Prospero then has Ariel bring Alonso and his retinue before him. While he is kind to Gonzalo, he criticizes Alonso for being cruel and Antonio for being overly ambitious. Prospero then reveals his true identity as the former Duke of Milan. As he sheds his sorcerer's garments, Prospero also cedes his powers. Alonso, recognizing the wrong he inflicted upon Prospero, restores Prospero's status as duke. Taking Alonso to Prospero's quarters, they find Ferdinand and Miranda playing chess. The ecstatic Alonso cannot believe his son survived.

Accompanied by the ship's master and boatswain, Ariel arrives and tells the incredulous king that the unharmed ship is docked in the harbor. The other conspirators, still clothed in stolen apparel, arrive as well. Caliban realizes his error regarding Stephano. Inviting Alonso's entourage to stay overnight with him, Prospero promises a full account of the intervening years since being deposed—tomorrow they set sail for Naples to prepare for the wedding between Ferdinand and Miranda.

Prospero grants Ariel his freedom. In the play's concluding epilogue, Prospero admits to ceding his magical powers, acknowledges the restoration of his dukedom, and—perhaps most crucially—forgives his enemies. The audience's applause, he states, will release him from the island and all the illusions it represents.