"Lying is universal--we all do it. Therefore, the wise thing is for us diligently to train ourselves to lie thoughtfully, judiciously; to lie with a good object, and not an evil one; to lie for others' advantage, and not our own; to lie healingly, charitably, humanely, not cruelly, hurtfully, maliciously; to lie gracefully and graciously, not awkwardly and clumsily; to lie firmly, frankly, squarely, with head erect, not haltingly, tortuously, with pusillanimous mien, as being ashamed of our high calling."
Satire or not, this essay explained "judicious" lying much better than the tired "Would you lie to Nazis about the location of any Jews you know?" or something. High school English class, conversations related to Kant, etc. Twain takes the idea lying, something most claim to hate and instead demand for transparency, and turns the Lie into a virtue. Lies make mankind civilized.
"The highest perfection of politeness is only a beautiful edifice, built, from the base to the dome, of grateful and gilded forms of charitable and unselfish lying." The exchange of "How are you?" "Fine, thank you." and all its all incarnations mostly come off as conversation fillers; with closer friends one may even tack on how they're actually doing, even if it's the exact opposite of "fine" (I know I'm guilty of it on occasion). But it's polite to show interest in someone else's well-being, even if you don't. And it's polite to answer as if you are willing to always tell them how you really feel.
Along with unselfish lies, Twain brings up silent lies. Sometimes it's easiest to say nothing to prevent getting trapped by your own words; however his examples focus on staying silent for the benefit of others. In some situations, there are trivial matters you don't mention for various reason, often boiling down to keeping the peace. Not that it works for everything. Silence after being asked the classic "Does this make my butt look big?" can never end well.
Lying is a tool that, according to Twain, should be used with good intentions and the benefit others instead of lying to bring others down for one's own benefit.