A massive part of the irony of this excellent novel lies in the way in which the events are narrated to us through the eyes of Huck. As an unreliable narrator who often is very innocent about the ways of the world and is also rather enamoured of his friend, Tom Sawyer, he often presents either his ignorance or confusion to his adult readership who understands precisely what he is talking about and sees the reality and truth of what he says in a different light. You might examine the comments Huck makes about religion in some of the earlier chapters as examples of this, especially when Huck talks about the Widow's "grumbling" over her food in Chapter One, which we of course understand to mean the grace that she is saying.
However, another important aspect of the irony is the way in which Huck always thinks that Tom Sawyer's ideas are better than his, whereas we in reality know that Huck is actually far more practical and logical than Tom, and that Tom's ideas are ridiculous and ludicrous in their romantic and elaborate nature. Consider how Huck responds to Tom's plan to free Jim:
Tom told me what his plan was, and I see in a minute it was worth fifteen of mine for style, and would make Jim just as free a man as mine would, and maybe get us all killed besides. So I was satisfied, and said we would waltz in on it.
In spite of the logical and sensible nature of Huck's plan, he thinks it comes second to Tom's because of the way that Tom's plan has much more "style" and endangers their lives. This is ironic because it creates a disparity between what Huck, our narrator, thinks to be true and what we as the audience know to be true.