Mark Twain is certainly a master of the use of hyperbole and understatement, and in this short essay, he makes extensive use of both of these techniques both for humour and to underline his point. Even the most cursory review of this essay reveals the presence of plenty of examples of both of these literary techniques, and so let us have a look at the beginning of the first paragraph to identify some examples.
Fifty years ago, when I was a boy of fifteen and helping to inhabit a Missourian village on the banks of the Mississippi, I had a friend whose society was very dear to me because I was forbidden by my mother to partake of it.
A great example of understatement could be considered to be the description of a friend, "whose society was very dear to me because I was forbidden by my mother to partake of it." The bathetic element in this sentence adds great humour to this phrase, as we are led to believe this friend is "dear" to Twain for more noble and laudable reasons than that which follows.
You might like to consider the following example of hyperbole as Twain continues to establish his point:
I am persuaded that a coldly-thought-out and independent verdict upon a fashion in clothes, or manners, or literature, or politics, or religion, or any other matter that is projected into the field of our notice and interest, is a most rare thing -- if it has indeed ever existed.
The end comment, that raises doubts as to whether logical formulations have ever existed in the history of man clearly indicates that this is an exaggeration for effect, deliberately trying to provoke his readers with this statement. This is of course Twain's typical style.