how did antonio get rid of his brother prospero and his daughter ? who saved them?how?

Prospero used to be the duke of Milan. Antonio, Prospero's brother, conspired with the Duke of Milan to usurp his throne. They basically set Prospero and his daughter out on a raft to be eaten by sharks or something. Fortunately Gonzalo leaves Prospero his handy magic books. Prospero and his daughter arrive on the island and Prospero sets up his magic kingdom. I suppose Gonzalo leaving the book helped save them but that is about it. Prospero is pretty excited to get his foes close to his magical realm. He creates the storm (Tempest) so he can get them on the island and set things straight.

Antonio was given to look after the affairs of Milan when Prospero indulged himself in the studies of Magic art, but Antonio became ambitious and gained absolute control by replacing Prospero's men with his.He joined hands with King of Naples, Alonso who was an old enemy of Prospero to remove his brother and crowned himself at the throne of Milan. A group of men headed by Gonzalo, a trustworthy associate of Alonso were given the task to put Prospero along with his daughter on a boat in the middle of the sea at the mercy of the sea. Touched by the pity as a little girl accompanied Prospero, Gonzalo supplied them with some food, clothes, water and the most important the books which Prospero regard above his dukedom to help him further to teach a lesson to those who did wrong to him betraying the trust of a brother for the sake of power and wealth.