Fiction writers have long wrestled with speech, language, and dialogue. From finding the exact word for the exact moment to controlling how the reader reads through punctuation, from dialogue where a memorable character's voice fills your head with their inflection and tone and exclamations to a simple declaratory phrase, like this one from The Lottery: "...and then they were upon her." You're horrified at the action, but it's the phrase which lives to haunt.
Distinguishing between the "narrator" of the story and the characters' dialogue generally means there are a number of voices at work simultaneously. Never forget, however, that there's always an author lurking in the background who is responsible. Our ability to "hear" characters, in their own language (diction), is a very difficult process for a writer. There must be no false cues, or if the narrator is telling what was said, the plausibility of what they recount of it is paramount.
In particular, several stories you'll read deal with language/diction in a number of very creative ways. Look at the straightforward southern dialect (regional language) of Sister in "Why I Live at the P.O.," but also notice that it's Sister who tells the reader all that Stella-Rondo supposedly says, as well as the title of "Everyday Use" which seems to underpin Dee Wangero's need for the now-fashionable historic "artifacts" she wants to preserve and display as "Art."
Dorothy Parker's story, "The Waltz," is a masterpiece of the marriage between writing and language: the interior monologue (thought) of the main character, juxtaposed against what she actually says in response to supposed questions the man asks that we never actually see (or hear). This trio of voices (the character's thoughts, her verbal responses to questions that we imagine on our own) form the three threads which match the rhythm and stately musicality of a traditional waltz in 3/4 time.
In Ernest Hemingway's "Hills Like White Elephants," dialogue between the characters is prominent, and in the forefront, but what they're discussing remains mostly a vague mystery. We get "clues" about the couple's discussion--"a simple, medical procedure"--that we begin to sense what they are discussing is likely a taboo subject, not legally, ethically, or morally up for discussion (abortion), and they, too, "dance" around the topic while the reader tries to piece together the jigsaw puzzle of their words.
"A Clean, Well-Lighted Place" might be the most difficult of these readings, because, again, we have an author, Hemingway, who loves to play with language. Here we have the story of an old, simple man who likes to sit at the cafe with his drink(s), juxtaposed against the young man who is impatient to close to go home to his wife. The story, however, deals primarily (as a thinly veiled treatise) with the topic of suicide. It's a "sin" to commit suicide; and as a Catholic (the story is set in Spain, a primarily Catholic nation) a mortal sin prevents you from entering heaven, receiving salvation, and the inability to be buried in hallowed, or sacred ground. He addresses both Catholicism and Christianity through his altered versions of both the "Hail Mary" and "The Lord's Prayer." Another masterpiece of an author handling language and writing and speech, providing a new interpretation of what constitutes "A Clean, Well-Lighted Place."
The obvious ethnicity of "Girl" makes this rather short story a powerful reminder of both race and gender and social stratification. A straightforward set of instructions/rules/guidelines from an older woman to a young girl broach a wide range of topics: mundane household duties (laundry); traditional skills like sewing, sexuality and public appearance, manners and etiquette, as well as traditional (ethnic) superstitions. A very modern take on dialogue (although it's really only a one-way conversation), without all of the encumbrances of traditional written dialogue (quotation marks and creating new paragraphs for each time the speaker changes), and still, somehow Kincaid manages to create a sophisticated story centered on gender, dialect and language.