How did Prospero and Miranda end up in the island years before the present action of the play?

In Act One, we are told that Antonio usurped Prospero's position while he was immersed in his study of the black arts. His intent was to kill his brother, as well as his niece, in order to gain Prospero's wealth and estate. Fortunately, those charges with the deed could not bring themselves to murder someone they believed to be a good man, so they set Prospero and Miranda adrift in an old boat on the open sea. The two miraculously survived and ended up on the island.