“It’s only a play” (Situational Irony)
When Miranda calls to her father, saying, “Oh God! Oh God! A sinking ship! Father help!! Prospero responds, “Come daughter, calm yourself, it’s only a play. There’s really nothing wrong” (Act 1, Scene 2). Prospero's comment calls attention to the theatricality of what is going on on stage, breaking the fourth wall and ironically suggesting that Miranda's concerns as a character are trumped by the fact that she is an actor in a play, and everything they are doing is a fiction.
Prospero is the ruler of the island (Dramatic Irony)
Prospero seeks to enact revenge on those who dethroned him by causing them to crash their ship on the island over which he has complete control. These nobles, however, have no idea that it is Prospero who created the storm, or that he is the ruler of the island. This creates an instance of dramatic irony in which the audience knows something the Neapolitan nobles do not.
Caliban's Plans to Revolt (Dramatic Irony)
Midway through the play, with the help of Trinculo and Stephano, Caliban makes plans to overthrow his master, Prospero. They travel across the island, planning a revolution. In this instance, the audience knows about the plans to rebel before Prospero does. Thus, this creates dramatic irony.
Prospero haunted by Caliban (Situational Irony)
Caliban's rebellion fails, and he is not granted the complete freedom and dominion over his island he had desired. However, he gets his revenge in subtler ways, when he haunts Prospero on the island. While Prospero maintains the structural "upper-hand" on the island, Caliban curses him, and Prospero is upset with the onslaught of opossums on his island, and the ways that nature is fighting back against his colonization of the land.