How does Shakespeare's The Tempest explore the theme of discovery?

In a sense, the theme of discovery is at the heart of Shakespeare's The Tempest. On the one hand, you have the shipwrecked crew stranded by the storm at the beginning of the play. Much of the rest of the play is concerned with the stranded characters discovering the strange and exotic island, complete with magic, spirits, and strange creatures. Likewise, another major component of the play focuses on Miranda's discovery of human society. Stranded on the island with her father and few other companions, Miranda has little knowledge of civilization or human nature. However, with the arrival of the shipwreck (and especially Ferdinand, her future husband), Miranda gradually discovers the intricacies of human society and relationships. 

Though you certainly don't need to make this connection, it's possible to link the play's theme of discovery to colonization. In some ways, Prospero can be seen as the prototype for the European who discovers and colonizes native populations, as he arrives on the island and presses Caliban into his service. Thus, though the theme of discovery is often exciting and fantastical within the context of the play, it also comments on the burgeoning European tendency to discover and exploit new lands.