These are the only 3 wizards that are mentioned in the book.
Gandalf the Grey- He is the wizard that helps the fellowship of the ring. He knows the dangers of taking on the dark powers, yet he knows that if it is not done middle earth is doomed. His fate I will not mention, you must read the book or watch the movie. He weilds the sword made by the elves called Glamdring. You can read a lot about him in The Hobbit.
Saruman the White- He turns to the Dark Lord, Sauron. Sauron gives his orders to Saruman and Saruman carries them out. Saruman tries to bring Gandalf the Grey under the Dark Lord's power, but Gandalf will not fall to Sauron. He actually plays a rather small part in the book, but a much larger part in the movie.
Radagast the Brown- He has a very small part, and only comes up twice. He tells Gandalf that the Nazgul are moving toward the Shire (or Hobbiton). At that same time, he takes the message to Gandalf that Saruman wants to talk to him. When the messengers are sent out from Rivendell, they stopped at his house and he was not there. This is hinting that Saruman has done something with Radagast.