One example of irony is that Huck considers himself evil because he does not pray. Although Huck has all the correct morals it is ironic that he thinks he is evil. So although Twain is saying that Huck is bad and does all this stuff that's wrong its only wrong because of how backwards society was. In reality Huck was average if not better spiritually than almost very other character. An example of Huck being "bad" in a not so bad way is when he decides to that he's going to aid Jim because he figures he is already going to hell so adding another 'sin' to his rap sheet can't hurt.
Another example of irony is that early in the story Huck was told he has to be good to be bad. "But Tom Sawyer he hunted me up and said he was going to start a band of robbers, and I might join if I would go back to the widow and be respectable". This is irony because the last thing a band of robbers is, is respectable. Therefore Huck having to be respectful, especially to someone he sees as authority is very ironic.
My last example of irony is that Huck's father gets mad at him, for going to school. This is irony because obviously school is a good thing but Twain is having pap get mad because he's a drunk that really has no future and the most narrow outlook on the world. Therefore by having Pap, the dumb drunk get mad about