Remember that "brevity is the soul of wit." Even your funniest ideas will ring hollow if you take too much time to express them. Being funny in a concise fashion often proves difficult, which explains why humor connoisseurs value one-liners so much. The British-American comedian Penny Youngman was famous for hard-hitting one-liners directed at his wife, like the following, which combines speech with gesture: "My wife's cooking is fit for a king." (Gestures as if feeding an invisible dog.) "Here King, here King!"
Pun occasionally. Oscar Wilde, whom biographer Richard Ellmann calls one of the wittiest men in literary London during the late 19th century, famously bragged that he could make a pun on any word. While you don't have to achieve Wilde's absolute mastery of the art, the occasional pun certainly helps to liven up your writing and make it more witty. Below are famous examples of puns by Wilde, Benjamin Franklin and Hilaire Belloc:
Oscar Wilde:
"Nothing succeeds like excess."
"Work is the curse of the drinking classes."
Benjamin Franklin:
"We must hang together, or assuredly we shall all hang separately."
Hilaire Belloc:
"His sins were scarlet, but his books were read."
Reword famous maxims and phrases, employing paradox when possible. The Oxford English Dictionary defines paradox as, "An apparently absurd or self-contradictory statement or proposition, or a strongly counter-intuitive one, which investigation, analysis, or explanation may nevertheless prove to be well-founded or true." An important part of wit is the ability to shock or amuse your audience by subverting received wisdom and conventional thinking. Wielding paradox allows you to accomplish this.
Both recent critics and the author's contemporaries acknowledged G.K. Chesterton as a master of paradox. You can see for yourself in the following examples:
"A man does not know what he is saying until he knows what he is not saying."
"A yawn is a silent shout."
"Ideas are dangerous, but the man to whom they are least dangerous is the man of ideas."