"The Lady with the Pet Dog" opens in the point of view of the man named Dmitri Dmitrich Gurov and remains in his point of view until the end. Therefore it would seem to be his story and to focus on his feelings, thoughts, perceptions, and behavior. The opening sentences are really masterfully crafted. They have been translated into English in many different ways.
It was said that a new person had appeared on the sea-front: a lady with a little dog. Dmitri Dmitritch Gurov, who had by then been a fortnight at Yalta, and so was fairly at home there, had begun to take an interest in new arrivals.
This establishes, at least for Russian readers, that the setting is Yalta and that everyone is so bored that the biggest topic of conversation is the arrival of a woman who walks her little dog on the promenade. It introduces both the man and the woman and foreshadows that he will probably find some way to meet her and hopefully cure his boredom by having an affair. It also introduces the pet dog, who will play an important role in their becoming acquainted and will then disappear from the story.
"If she is here alone without a husband or friends, it wouldn't be amiss to make her acquaintance," Gurov reflected.
Chekhov establishes that Gurov is a philanderer and that he has an unhappy relationship with his wife, who doesn't respect and who probably doesn't care what he does when he is away from home. Gurov is experienced with extramarital affairs; Anna Sergeevna von Diederitz is not. Gurov initiates the relationship by getting her little dog to bark at him.
Afterwards he thought about her in his room at the hotel--thought she would certainly meet him next day; it would be sure to happen. As he got into bed he thought how lately she had been a girl at school, doing lessons like his own daughter; he recalled the diffidence, the angularity, that was still manifest in her laugh and her manner of talking with a stranger.
Chekhov goes freely into Gurov's mind. It is Gurov's story. He is a middle-aged man, while Anna is still young. He falls in love with her because of her youth and relative innocence. Anna Sergeevna also has an unhappy marriage, but the reader is not told much about her own thoughts or feelings. Chekhov does not enter her mind but only narrates what she says and does. When they finally have to separate, Anna goes way off to some provincial city, but the reader is taken to Moscow with Gurov and sees nothing of Anna until Gurov makes the rash decision to travel to the distant city of S-- just to talk to her again. Gurov is undoubtedly the protagonist and the viewpoint character throughout. Nothing would have happened at Yalta if he hadn't initiated it. Nothing would have happened after Yalta if he hadn't initiated it.
At the very end of the story, when the man and woman are thoroughly bonded together, Chekhov speaks of both of them almost as if they are one person. In this last sentence both characters' thoughts and feelings are described simultaneously.
And it seemed as though in a little while the solution would be found, and then a new and splendid life would begin; and it was clear to both of them that they had still a long, long way to go, and that the most complicated and difficult part of it was only just beginning.