The most basic type of conflict is that which pits one character against another. Think of Robin Hood versus the Sheriff of Nottingham. The drama is built around the conflict between these two characters. The opening line of author Stephen King's novel, "The Gunslinger" quickly identifies the character against character conflict that drives his whole "Dark Tower" epic. It is, "The man in black fled across the desert and the gunslinger followed."
Many epic sagas involve the character versus nature conflict. The 2000 movie, "The Perfect Storm," is a recent example of a nearly pure conflict of this type. Ernest Hemingway's last novel, "The Old Man and the Sea," introduces what will be the prime conflict of the story with the sentence, "He was an old man who fished alone in a skiff in the Gulf Stream and he had gone eighty-four days now without taking a fish." The whole story is a development of the consequences of that sentence.
The conflict between a character and himself is the theme of many stories featuring what is popularly called an antihero, or a character seeking redemption. The conflict can be subtle or overt. Most stories have at least an element of this conflict because the lead character must overcome some deficiency or fear in himself. One of the most overt cases of this theme being played out is in Robert Louis Stevenson's novella, "Dr. Jekyll and Mr. Hyde." From the first chapter, Stevenson writes of each character in terms of their faults and virtues, intimating the type of conflict that is to come. In the second chapter, a character comments that "...it is more than ten years since Henry Jekyll became too fanciful for me. He began to go wrong, wrong in mind." With these two sentences, the early intimations coalesce into exactly the type of conflict that dominates the book.
Almost every piece of literature invites the reader to see things from the perspective of the protagonist. In his classic work, "1984," George Orwell uses this knowledge to introduce the reader to this conflict in a masterfully subtle way with the opening sentence, "It was a bright cold day in April, and the clocks were striking thirteen." The reader immediately knows there is something terribly askew with this society. As the novel develops, the first jarring hint of a dystopian society is fully developed.