Mark Twain says in the first paragraph of the story that his friend asked him to look up a friend by the name of Rev. Leonidas Smiley, knowing that he would meet a storyteller who would tell him about a man named Jim Smiley, a notorious gambler from the area. He then tells the reader that this storyteller would,
"....bore me to death with some infernal reminiscence of him as long and tedious as it should be useless to me. " (paragraph 1)
Ironically, he then goes on to tell us this story that was so BORING to him with the idea that it would entertain us. It does entertain us and has for generations. This story that was"useless to me" was Mark Twain's first big success and actually was the title story in his first book published in 1897, The Celebrated Jumping Frog of Calaveras County and Other Sketches. So the irony is that it isn't boring, but totally entertaining, and it isn't useless to him, but skyrocketed him on a road to success.
The main irony in "The Celebrated Jumping Frog of Calaveras County" is that Jim Smiley is outfoxed by the stranger. According to Simon Wheeler:
Smiley was monstrous proud of his frog, and well he might be, for fellers that had traveled and been everywheres, all said he laid over any frog that ever they see.
Well, Smiley kept the beast in a little lattice box, and he used to fetch him down town sometimes and lay for a bet.
The essential irony is that Smiley knows he had the best jumping frog in the country and perhaps in the world. He makes money by bringing the frog into town where he will "lay for a bet." That is to say, Smiley is looking for a sucker who will bet against him. Wheeler has specified that Smiley's frog is very ordinary looking. Smiley thinks he is sure to win the bet he makes with the stranger, especially since Smiley goes out and personally catches a frog for the stranger to bet on. The irony is that the stranger is not such a sucker as he appears to be. While Smiley is looking for another frog, the stranger fills Smiley's frog Daniel Webster full of quail shot, and when the contest begins, poor Daniel Webster can't even get off the ground. Smiley loses forty dollars. This is a typical story of a trickster out-tricked. Such stories were popular in Mark Twain's day. William Faulkner uses similar anecdotes in some of his novels, notably in the trilogy featuring Flem Snopes: The Hamlet, The Town, and The Mansion.