The Narrator/Magician
The Narrator asks us to trust him as he tells us the story of Elmyr and Irving. Doing his best to reveal the truth of their trickery throughout the film. He later becomes The Magician when telling us the story of Picasso, Oja and her grandfather. All of which we learn is a lie.
The Girl
We see The Girl early in the film, and it's not until the final act that she returns to fulfill the Narrator's promise to share her story. She becomes the inspiration for Picasso's new work, and the central figure in the scandal involving the sale of these paintings which were forgeries created by her grandfather.
Elmyr
Elmyr is an art forger who lives on the island of Ibiza, and attempts to live a lavish and stylish life. On the surface he is chic and charming and appears to be everyone's friend. But underneath it all he is lacking the touch of truth, and it appears that he has made himself into a living breathing forgery, just like one of his paintings.
Clifford Irving
Irving wrote a book about Elmyr's life of forgery, and soon after spending time with him decided to write another book. This one about Howard Hughes. But we come to find out that the tables have turned and Irving appears to have taken what he has learned from Elmyr about forgery and created Hughes' autobiography in a similar fashion. Throughout the film, Irving is accusatory about Elmyr's falso life and work, all of it seeming to be smoke and mirrors in order that no one will notice that he is cut from the same cloth.