Alonso (the King of Naples), his brother Sebastian, his son Ferdinand, Antonio's counselor Gonzalo, and Antonio (brother of Prospero, the usurped Duke of Milan) are on a ship with sailors caught in a tempest at sea. The storm scares all of the nobleman to abandon ship, fearing it split in half. When the storm subsides, the exiled Duke Prospero and his daughter Miranda appear on the island they have inhabited for 12 years. Miranda tells him she saw the ship crack in the storm, but Prospero calms her, explaining it was a magical illusion he created. He explains he was once Duke of Milan, but his brother Antonio took over when he began deeply studying literature, eventually teaming with Alonso to banish Prospero and Miranda and abandon them at sea, where they luckily landed on the island and survived since Gonzalo had given Prospero money, clothes, and his sorcerer books in the boat. Now, he explains, his enemies have sailed by, so he created the tempest to shipwreck them. He causes her to sleep and calls his spirit Ariel to come. Ariel verifies that the nobles are safe on the island, while their ship is deep in a hidden harbor with the crew asleep; further, the remainder of the fleet has returned to Naples believing Alonso is dead. We learn that Prospero rescued Ariel from the "foul witch" Sycorax and will free Ariel himself when his plans for the nobles are complete. Sycorax had imprisoned Ariel in a tree for refusing to do her evil, then, after her death, Prospero freed him. She also had a deformed son, Caliban, whom Prospero commands as his slave (Note that Caliban anagrams from a slightly misspelled canibal). Hidden, Ariel sings a song and scares Alonso's son Ferdinand as he wanders around the island, eventually meeting Prospero and Miranda. Both Miranda and Ferdinand immediately fall in love, but Prospero (although approving) pretends to be gruff and critical toward Ferdinand.
In another part of the island, Alonso, Sebastian, Antonio, Gonzalo, and the lords Adrian and Francisco are wandering. Alonso fears Ferdinand is dead, but Gonzalo assures him he may be living, since they are living. Ariel causes all to sleep, except Sebastian and Antonio. Then, Antonio convinces Sebastian to kill Alonso, so Sebastian will become heir to Naples' throne. Prospero, though, has Ariel awaken Gonzalo to warn Alonso. Elsewhere, Caliban is gathering wood when the jester Trinculo, then the drunkard Stephano (both from the ship) come upon them. Caliban takes Stephano to be a god (the Man in the Moon), and vows to serve him.
At Prospero's cave, Miranda meets Ferdinand carrying logs for her father. Here they exchange their love for one another and vow to be married. Prospero, watching in secret, approves. Elsewhere, Caliban convinces Stephano to kill Prospero and seize Miranda so they can be king and queen. Ariel, though, overhears and will warn Prospero. Alonso and others are wandering when Ariel and other spirits bring in a table of food. Before they can eat, Ariel appears and takes the food away, then informs Alonso, Sebastian, and Antonio that it is their evilness toward Prospero that has caused their current sorrows (shipwreck, loss of Ferdinand, etc.).
At the cave, Prospero presents Miranda to Ferdinand, though instructing him not to "break her virgin-knot" until after they are properly married. He celebrates by presenting them with a show by the spirits Iris, Ceres, and Juno. However, Caliban, Stephano, and Trinculo show up to kill Prospero. He, however, creates a distraction with extravagant garments, then sends the fairies after them like hounds hunting foxes.
In the final act, Prospero brings the nobles to his cell and reveals himself to them. He forgives Alonso, Antonio, and Sebastian then reveals that Ferdinand is safe with Miranda. Alonso restores Prospero's dukedom and Prospero promises to return all home safely to Italy. As for Caliban, he promises to mend his ways while Stephano and Trinculo repent for plotting to kill Prospero.