How do Prospero and Miranda end up on the island in Act 1?

In Act I, Prospero tells Miranda that Antonio allied himself with the King of Naples (Alonso) and then arranged for a military coup during which they were kidnapped. When Miranda asks why they weren't killed, Prospero says the people of Milan loved him too much for Antonio to risk being condemned for their murders, and instead he cast them adrift in a rickety boat. He adds that the boat was stocked with a few provisions as well as some of Prospero's precious books by a loyal lord of Milan, Gonzalo, and goes on to say that after being cast adrift he and Miranda arrived on the island and there made their home.