How do authors build conflict in literature? Well, in lots of different ways. Conflict can occur between two characters, like the struggle between Victor Frankenstein and the Monster in Mary Shelley's novel Frankenstein. Often these scenarios will play out as a struggle between protagonist and antagonist.
Or a character can be in conflict with an external force like nature or society in general. Macbeth, for example, seems to be struggling against time. J.D. Salinger's oh-so-alienated protagonist Holden Caulfield is in conflict with society in The Catcher in the Rye. In Mark Twain's Adventures of Huckleberry Finn, Huck bumps up against the rules and order of the antebellum South.
Conflict can be internal, too. Lots of novels are interested in their protagonist's inner struggles, such as those of Humbert Humbert in Vladimir Nabokov's Lolita or Henry Fleming in Stephen Crane's The Red Badge of Courage.
Needless to say, a novel or play can have many different kinds of conflict propelling the plot, some subtler than others. As we here at Shmoop like to say, the more conflict the better.