The main conflict in the story is Gurov's struggle to find meaning, truth, and beauty in a world that so often feels devoid of them. Gurov's brief dalliance with the titular lady with a pet dog has opened up new horizons for him, but so long as he remains stuck in his current life, he has no opportunity to explore them in any depth. To compound the problem, Gurov recognizes this as an ever-present conflict in most people's lives—one that they never seem to resolve.

By the close of the story, there's no sense that Gurov has managed to resolve this conundrum. He's got it into his head that the only way that he can find meaning, truth, and beauty in his life is by being with Anna, yet it's by no means apparent that this strategy for dealing with life's ugliness will succeed. The potential is there, undoubtedly, but as Chekhov makes clear right at the end, Gurov and Anna are only just beginning on the most difficult part of their relationship. That may be a resolution of sorts, but if so, it's a very strange one indeed.

Part 1 is the exposition of the plot. This is where we meet our two main characters and where they meet each other. The rising action occurs in Part 2 when the couple begins their affair. At the end of Part 2, each person goes back to his/her own life, and Gurov believes the affair to be over, just as the others in the past have been. This is part of the rising action leading up to the climax. Part 3 continues the rising action, and Gurov realizes he can't forget Anna and truly loves her. When he goes to where she lives and finds her at the opera, she tells him she hasn't been able to forget him either and agrees to come to Moscow. In Part 4, we learn that Anna has been coming to Moscow off and on for a while, but we don't see the climax until Gurov looks in the mirror and notices how he has physically changed. The change in his outward appearance reflects his inward change as well. This is the climax because we now know that Gurov is going to have a life with Anna. He tells her that they will be together one day, even though they have big obstacles to overcome.

The main conflict is whether Anna and Gurov have any kind of future together. They are both married, and having to sneak around is taking its toll on them, especially Anna. Once we know the outcome of this conflict, then you have the resolution.