Examples of realism include the setting, the characters, and the themes of the story. Joyce was very much a "realist" writer.
The setting of the story is a dark and dank neighborhood in Dublin, Ireland. The houses are similar and box-ish. The story most likely takes place in the early 1900's. It is a very realistic setting, as many neighborhoods in Dublin were like this.
The characters were also very realistic. The narrator is a young boy who acts like any young boy that age would while experiencing his first big "crush." He became rather obsessed with his friend's sister and ignored everything else in his life to only think about her! The other characters are just as realistic and plausible, including the aunt and uncle the narrator lives with.
The themes are also very realistic in that the narrator learns a valuable, but sobering lesson, about how he has wasted much of his time obsessing over someone he should not have been obsessing over and how life is SO much more complex than what he originally thought it was:
As he walks slowly out of the hall amid the darkening of the lights, he thinks that he is a "creature driven and derided by vanity" and his "eyes burned with anguish and anger." (eNotes)