Christopher Nolan's film very much connects his style of film-making and storytelling. Nolan's images always look and feel very real, as though we watching could be there with the characters ourselves. From the opening image of a multitude of magician's top hats strewn about on the forest bed, to Cutter showing Jess a magic trick with a canary - the imagery looks like life, and thus allows the audience to enter the story in a way where they are apart off it rather than being separated from it because of the imagery.
Nolan also uses handheld camera shots and dramatic movement to create a kinetic energy for specific moments in the film. The opening scene with handheld shows us eventually the delicacy of the lie Cutter has perpetrated on the young Jess, and the sweeping camera movement during Angier's drowning from a wide shot to a close up of Jackman's character drowning engages the audience in a way that enlivens their emotions in specific ways. The unsteadiness of the handheld represents the balancing act of the lie. The energy of the movement reveals the life and death weight of the drowning.
Finally, Nolan utilizes his signature misdirection as he does so well (see also Memento, Interstellar and Inception). He allows the narrative itself to be a magic trick where not all is revealed until the last act, or "the prestige" part of the film. Here we learn the dual nature of Borden and Angier's monstrosity. These reveals are both unexpected and obvious once we piece together everything that Nolan's storytelling has revealed, but the mystery is able to be kept because this type of storytelling has the audience considering that it could go in many different directions. This keeps the audience engaged as they are participating in solving the puzzle that Nolan crafts for them.