An auteur is a filmmaker who has his own unique "style" that shines through in his projects, usually because of the amount of creative control he has.
While this could apply to most famous filmmakers, it is usually only used to talk about directors with extremely and instantly recognisable affectations in their style that are as good as a signature, "This belongs to Wes Anderson" or "This film is a Martin Scorsese picture".
Anderson's quirks, tricks, techniques, and stylistic elements should be obvious. Take a look in imdb's trivia sections on his films or Anderson himself and look for director trademarks. Check wikipedia for similar comments or lists. Your local library might have a book on Anderson or other "auteurs". Best of all, though, take an afternoon and watch three or four of his films (they're not long). Note things like cinematography (how the camera moves), sound and music (and how it interacts with the visuals), shot composition, actors' performances, colours, costumes, set construction, effects (and how they're used, what they look like, etc.), and so on. Just start thinking about the elements of film. You'll have to actively watch and take notes, maybe rewind and rew111catch scenes. You can't throw the movie on and then flick back-and-forth between the film and your texts/ facebook.
You should also look at a couple of other auteur filmmakers to maybe compare/ contrast their unique voices and visions to Anderson's voice and vision. Try Terry Gilliam, Tim Burton, Martin Scorsese, Hayao Miyazaki, Sergio Leone, David Lynch, and John Waters.

He'd never ask someone to do his homework for him.
Can't stop the signal.