What sentences establish the style of "A Clean, Well-Lighted Place" by Hemingway? What is distinctive about them?
It is always the opening sentences that set the style of well written literature. In this case, the opening sentences include the narration and dialogue as in this excerpt from the opening narration and dialogue:
The two waiters inside the cafe knew that the old man was a little drunk, and while he was a good client they knew that if he became too drunk he would leave without paying, so they kept watch on him.
"Last week he tried to commit suicide," one waiter said.
"He was in despair."
The distinctive diction techniques here are Hemingway's trademarks found in all his major works. The story is written in the style of minimalism in which only the most essential story and diction elements are given or used: Hemingway routinely left more untold than told in his stories. One distinction in vocabulary choice to note is there are few adjectives or adverbs used (adjectives modify nouns, adverbs modify verbs and adjectives). Those that are used are simple ones derived from Old English like "little" or "good" in the quote above. Another distinctive point of style is that Hemingway lets characters' actions and dialogue reveal their character traits. For example, the old man is drunk and the waiters keep watch. Without reading any further, this tells you that the old man is unhappy and the waiters work well together and are attentive to both the customer and the integrity of the business.
Another distinctive technique of Heminway's is symbolic narrative description. He introduces into his brief descriptions symbolism that helps lay the themes, the relationships between characters, the conflict, the tone of the narrator and mood of the story. In the first sentence, Hemingway introduces the symbolic motif of "the shadow the leaves of the tree made against the electric light." This will occur again and symbolizes the theme of how to avoid existential nihilism's despair and destruction: how to find order and meaning without living in despair.