How does Shakespeare present good and evil in the play?

For the most part, he doesn't. By that I mean, Shakespeare gives us a tale of political power, magical power, and vengeance   but a lot of the play doesn't have much to do with good or evil. Instead, it has to do with rightful places (Prospero is deposed), rights to power (Caliban claims the island should be his), and duty.
To the extent that good and evil are shown in the play, they are shown to be changeable, and to depend on character and situation. Prospero's power is extreme, and he could do much evil with it, but he sets it aside at the end, for example.