The prose in "The Lady with the Dog" is powerful stuff. Chekhov says what he wants to say exactly how he wants to say it, and he generally gets it done without wasting words or time. Think how much we know about Gurov from a short paragraph like this one:
Experience often repeated, truly bitter experience, had taught him long ago that with decent people, especially Moscow people – always slow to move and irresolute – every intimacy, which at first so agreeably diversifies life and appears a light and charming adventure, inevitably grows into a regular problem of extreme intricacy, and in the long run the situation becomes unbearable. But at every fresh meeting with an interesting woman this experience seemed to slip out of his memory, and he was eager for life, and everything seemed simple and amusing. (1.6)
We learn about his past, we're in tune with his psychological motivations for pursuing an affair in the first place, and we foresee a problem arising with Anna. We don't know about you, but that probably would have taken us 2-3 pages to explain.
Because so much of "The Lady with the Dog" is straightforward, you want to keep an eye out for those slightly more lyrical passages. There are only a few, so they tend to jump off the page. Consider passages 2.28 and 4.5. What do these add to the story? Are they warranted, given the context?