I think for me the funniest moments come as a result of the farce that characterises the relationship between Mrs. Popov and Smirnov. For example, the duel scene is an excellent example of farce and how it operates. Mrs. Popov is full of her emotion and is literally carried away by it, and contemplates duelling Smirnov, even though she has never shot a pistol before in her life. Consider what she says to Smirnov:
But before we start, you'd better show me how it's done. I'm not too familiar with these things. In fact I never gave a pistol a second look.
The way that Smirnov plays along with her absurdities whilst secretly becoming more and more mesmerised by her beauty, whilst she continues to plan on having a duel with him presents the true farcical nature of the play. This is why Smirnov on the one hand shows her how to fire a pistol so that she is able to shoot at him whilst in the next sentence offers an aside that shows how he is enraptured more and more by her character:
You hold it this way. (Aside) My Lord, what eyes she has! They're setting me on fire.
Such farcical situations create the humour in the play, which is further augmented by the way that they suddenly fall into each others' arms at the end of the play. This is farce, or, as Chekov put it, "A Joke in One Act."