Prospero was one a powerful Duke. A plot by his brother Antonio sees him thrown out of his kingdom with his baby, Miranda, and set adrift in a boat, with only the barest of necessities (provided by Lord Gonzalo). He is shipwrecked on an island for 12 years. Thanks to the books put on the boat by Gonzalo, he develops magical powers. We learn all this after a storm shipwrecks all of Prospero's enemies on the island; alongside Antonio, there is Alonso (the King who helped to overthrow Prospero), his brother Sebastian and son Ferdinand.
The storm was created for Prospero by Ariel, a spirit he freed from a spell. Prospero's plan is to marry Miranda to Ferdinand (ensuring his succession) and get his revenge. When Miranda meets Ferdinand, they immediately fall in love. However Prospero, to test the true nature of Ferdinand's love, pretends to be angry and sets him a demeaning task.
Alonso and the court are lost on the island, searching vainly for Ferdinand. Ariel's spell makes them sleep - except Antonio and Sebastian. Antonio encourages Sebastian to kill Alonso while he sleeps - but as they set about the assassination, Ariel intervenes to prevent it.
The only other inhabitant of the island is Caliban - a wild creature who abused the trust Prospero gave him by trying to rape Miranda. As a result, Prospero is punishing him with menial tasks. Caliban is discovered by Trinculo and then by Stephano, Alonso's butler. Stephano, who escaped drowning by floating on a barrel of wine, is drunk. He gets Caliban and Trinculo drunk too. Caliban offers to become their slave and show them the beauties of the island - if they will kill Prospero. They readily agree and set off to find him.
Three plots of romance, revenge and riot are thus set in motion. While magic brings them all together, it is only by renouncing his power and his magic (his final act in the play) that Prospero is able to achieve the restoration and reconciliation he is looking for. Whether his abusers will accept his forgiveness is another matter...