What (not whom) is the target of Twain's criticism and what techniques does he employ to achieve this satire?
Society's hypocrisy is the target of Twain's criticism. From promoting slavery as morally right to killing children in the name of a feud (which supposedly upholds family pride), Twain's satire leaves few aspects of American society unsinged. His message through Huck Finn is that humans have consciences which should guide them morally, but society corrupts the conscience and uses it for approbation of all that it once abhorred.
Twain's satire in Huck follows the four standard elements of classical satirical writing: hyperbole, reversal, parody, and incongruity.
In addition to the previous posts, I think Twain is also satirizing the Romantic/Transcendental philosophies saying the man can perfect himself. He focuses a lot on man's innate evil nature, such as is displayed in "The Man that Corrupted Hadleyburg" as well as other later works. Twain seems to mock the idea of moral perfect as well as the religious sentimentalism that came with Transcendentalism (Gargerford's poetry in Huck Finn is one example). He shows it as being ridiculous and nonsensical, adding a harsher, more biting form of satire as he got older.
There are many targets of Twain's satire in this work. The hypocrisy of human nature is just part of it...he also makes fun of the organization of religion, of con artists and their gullible victims, of pride and vanity, and the lopsidedness of slavery (which is what makes this coming-of-age book so amazing...it illustrates the true friendship of a little white boy with an adult black man and Huck's trouble with what he feels vs. what society tells him is right).
I agree with others that Twain is really satirising so many aspects of Southern American society. The Grangerford incident really satirised the kind of feuds that existed between Southern families - note how both the Grangerfords and the Shephertons bring guns to the service and listen to the sermon, which is on brotherly love, and then go back, discussing the sermon, but obviously not letting it penetrate their hearts at all!
Echoing the previous post's sentiment, I would suggest that Twain is quite skilled at being able to express what is in the hopes of what can be. I think this is fairly compelling and a strong idea given the nature and scope of his work. He seeks to present what is accepted as commonplace and tears the facade off it to expose a reality that strives and demands to be changed into what can be.
One of the classic examples of satire is Twain's description of Emmaline Grangerford and her obsession with writing weepy confessional poetry. Huck is utterly flummoxed by Emmaline and her behavior, which is described in such a way as to satirize those who cling to the Romantic tradition of literature, but he figures that she must be extremely talented to do the things she does.
We are each and all responsible for our own behavior, no matter what society says is "moral" or "right". This seems to be the message that underlays the novel and the point of much of the novel's satire. Huck is disturbed by the difference between society's mores and his own sense of loyalty, integrity, and honor.