In “The Tempest,” Prospero had lived on the island for 12 years before causing the shipwreck. He arrived there after his brother Antonio usurped him as Duke of Milan and set him adrift with his young daughter, Miranda.
Prospero and Miranda survived and reached a remote island. During those twelve years, Prospero studied magic, freed the spirit Ariel from imprisonment, and took control of Caliban, the island’s original human inhabitant. Miranda grew from a small child into a young woman there, knowing almost nothing of the wider world.
The shipwreck is not an accident: Prospero creates the storm when Antonio, Alonso, and their companions sail nearby. He uses Ariel’s magic to scatter the passengers across the island, beginning his plan for revenge and eventual forgiveness.
A common mix-up is confusing the twelve years with Miranda’s age. She was about three when she and Prospero were exiled, so she has spent those same twelve years on the island. The play’s main action then unfolds over roughly one day.