There are plenty of examples of realism in The Red Badge of Courage. Here I've provided analysis of some significant quotations that demonstrate realism in the novel.
Examples of Realism
Quotation: He felt that in this crisis his laws of life were useless. Whatever he had learned of himself was here of no avail. He was an unknown quantity. He saw that he would again be obliged to experiment as he had in early youth. He must accumulate information of himself, and meanwhile he resolved to remain close upon his guard lest those qualities of which he knew nothing should everlastingly disgrace him.
Analysis: Crane examines the psychology of a soldier. Unlike romantic war accounts that portray heroes bravely going into battle, Henry has no idea whether or not he has what it takes to fight. It reminds me of something Mike Tyson said when he was in his prime: "Everybody has a plan until I punch him in the face." Henry realizes that until he faces that first shot, he is uncertain how he will react.
Quotation: The captain of the youth's company had been killed in an early part of the action. His body lay stretched out in the position of a tired man resting, but upon his face there was an astonished and sorrowful look, as if he thought some friend had done him an ill turn. The babbling man was grazed by a shot that made the blood stream widely down his face. He clapped both hands to his head. “Oh!" he said, and ran. Another grunted suddenly as if a club had struck him in the stomach.
Analysis: Crane's realistic depictions of soldiers in battle serve to create a realistic war novel. There are no gasping of last words, clever quips, or philosophizing of death. The reader sees men being shot and dying. This non-heroic portrayal of death is made clear as Jim Conklin fears dying and being run over by artillery wagons.
Quotation: As he gazed around him the youth felt a flash of astonishment at the blue, pure sky and the sun gleaming on the trees and fields. It was surprising that Nature had gone tranquilly on with her golden process in the midst of so much devilment.
Analysis: Crane shows nature's indifference to the bloody battle, an indifference heretofore unrealized by Henry.
Quotation: They gazed about them with looks of uplifted pride, feeling new trust in the grim, always confident weapons in their hands. And they were men.
Analysis: Crane portrays realistic heroes, confident men, sure of their abilities as opposed to the gallant men portrayed in romantic tales of war.
Quotation: He had burned several times to enlist. Tales of great movements shook the land. They might not be distinctly Homeric, but there seemed to be much glory in them. He had read of marches, sieges, conflicts, and he had longed to see it all. His busy mind had drawn for him large pictures extravagant in color, lurid with breathless deeds.
Analysis: Crane's realistic portrayal of war stands out in comparison to Henry's unrealistic notions of battle. It's similar to when you were in Junior High School and expected all the guys and girls to look like the characters in High School Musical and then you realized after about 5 minutes that your schoolmates were the same old dorks you went to Junior High with.