Huck pretends to be someone else and tells a fabricated story about why his steamboat took so long to reach its destination. He explains a cylinder blew up, causing the delay. Mrs. Phelps wants to know if anyone was hurt. Huck explains that no one was hurt and then goes on to say that a black person was killed. Mrs. Phelps is happy to hear this because she knows having a cylinder explode can be very dangerous.

The fact that Mrs. Phelps does not view the death of an African-American as a tragedy is ironic, because we as readers view it as a loss of human life while Mrs. Phelps does not.

How does Twain use irony in the discussion between Huck and Mrs. Phelps about the "steamboat accident" in The Adventures of Huckleberry Finn?  

The episode in question here features Huck telling a story to Mrs. Phelps regarding a fictional steamboat accident. 

Huck tells the story to explain why he was delayed in his arrival and says that a steamboat accident was the cause of the delay. 

When Mrs. Phelps asks if anyone was hurt in the accident, Huck replies that no one was hurt, only one African American died. 

The irony here is in the double meaning of the term "no one" as it implies two, contradictory ideas. 

This statement is ironic because it equates the phrase "no one" with the idea of African Americans, suggesting that African Americans are not people or at least are not worth the consideration generally afforded to "real people". African Americans are real people and this fact provides some of the irony. 

Additionally, when Huck says that "no one died" he is telling a sort of truth. No one dies in the accident because the accident is a fiction. There was no accident, so no one could have died in it. This adds another layer of meaning to Huck's statement. 

Finally, we see Huck playing on conventional thinking in this turn of phrase. He knows how Mrs. Phelps will react and uses her conventional thinking to his advantage. The clear implication that Huck does not entirely agree with the conventional evaluation of African Americans as non-entities or as property makes Huck's speech a performance. 

Huck presents himself in a way that he knows will be accepted without criticism and in doing so creates a situation of irony. He does not mean what he says and the audience (the reader) understands this.