In The Tempest, what are the different styles of speaking of the main characters?
If you are trying to identify characters through their style of speech, then you need to pay attention to a number of different aspects of speech. Key to focus on are the choice of words, the tone and the attitudes expressed through speech. Bearing this in mind will greatly help you attach certain speeches to certain characters. Obviously, what will help you to answer this question is a very intimate knowledge of the text, where you understand the different relations between characters in the play, and in particular how power impacts those relations.
Key to remember is that Prospero is the central character of the play, who is shown to possess complete power through his magic arts over all other characters. As a result, he speaks with a defiant, lordly tone reflecting his station. His various servants adopt language that reflects their position, so the language of Ariel and Caliban can be identified by the tone of deference in the first case and sullen rebellion in the second. Miranda is a character who can be identified through her innocence and sense of love or her father, and the other characters who have entered this magical island variously express themselves in terms of wonder and practicality, which of course gives us key insights into their character.
Above all, knowing the various characters and the kind of traits that they possess will help you identify them from the kind of things they say and the attitudes they express. I have included a few links below to the enotes study section of this novel that I hope you will find useful.