The irony in this story is directly related to the title: "How Much Land Does a Man Need?" Throughout the story, Pakom wants more and more land for his money, and he would have the reader believe that he "needs" this land, when in reality this is simply a result of his excessive greed.

He continues to try and acquire more and more land, showing that he is never satisfied and will convince himself that he needs more and more when in reality he simply has excessive wants. The end result is him dying of exhaustion on the land he is trying to claim. When a simple grave is dug for him, the question is finally answered. No matter how much land a man wants, he only really needs six feet, enough to bury him in.

This is a reference to the futility of man's work—that no matter how lofty your goals, how high your greed, or how successful you are, in the end, it is all lost as we end up buried in the ground.

The ongoing irony in "How Much Land Does a Man Need" has to do with the fact that Pakom cannot stop trying to enlarge the amount of land he is going to acquire for his one thousand roubles. He keeps walking farther and farther, trying to enclose more and more of the rich land. He inevitably ends up getting into time trouble because the sun is setting and he is a long distance from the point he has to reach in order to make a complete circuit of the land he wishes to acquire. He has already tired himself out with his long day's walking, and then he is forced to walk faster and faster and finally to start running in order to reach his goal. The final irony is contained in the very last words of Tolstoy's story:

His servant picked up the spade and dug a grave long enough for Pahom to lie in, and buried him in it. Six feet from his head to his heels was all he needed.

That answers the question asked in the title, "How Much Land Does a Man Need?"

What is the irony in the story "How Much Land Does a Man Require?" by Leo Tolstoy?

Though there are multiple ironies in Tolstoy’s “How Much Land Does A Man Need?,” the central irony is dramatic irony. The reader is informed mere paragraphs into the story that Pahom is going to meet his downfall through his greed for more land when the Devil reacts to Pahom’s boast that he would not fear the Devil if he were to receive enough land. The Devil’s purpose in the story, in fact, is to bring this downfall about through multiple disguises. Thus, the reader is left to question how long it will be before Pahom is completely destroyed, while Pahom has no idea of the Devil’s plot against him.

When Pahom finally dies at the end of the story and the Devil laughs over his body before having him buried, Tolstoy chooses to answer the question that the title asks by saying only six feet is required, further emphasizing the tragedy of Pahom’s destruction.

What is the irony in the story "How Much Land Does a Man Require?" by Leo Tolstoy?

There are several ironies in Tolstoy's short story "How Much Land Does a Man Require?" (traditionally translated "Need").  The first is dramatic irony, a contrast between what Pahom thinks is happening and what we (readers) know to be true.  Pahom and his wife are adamant in a discussion early in the story that living a more rural, simple life is much better than a life in the city because they are not tempted to participate in the Devil's activities so rife in the cities.  Pahom's only complaint is that he could do so much more if he had more land, and he and his family go through several moves in an attempt to attain that goal.  He boasts that he wouldn't be afraid of the Devil himself if he just had enough land.  The Devil overheard him and tricked Pahom, playing on his greed, into actions which lead to his death.  We recognize the Devil at work, but Pahom does not.

Another example of irony in this story is situational irony--a contrast between what we and the characters expectto happen and what does happen in this story. The deal which Pahom made is to pay 1,000 rubles for whatever land he can walk around in one day; after he was tricked by the Devil and beaten by his own greed, Pahom did end up with all the land he needed--literally.  Six feet of land on which to be buried.  

Ironies generally point readers to the themes of a work; in this case, that greed is no way to gain happiness, that taunting the Devil is not going to turn out well, and that all we really needis enough to meet our basic neccessities--in this case, land enough on which to be buried.    

I've included an excellent e-notes summary below, as well, which I think you'll find helpful.