Try this at home

How writers come across as witty: some of it you can't explain; it's just talent. Here's the part that you can.

ALLUSION: "If you take this parking place, it'll be World War II all over again."
AMPLIFICATION: Names something, then puts additional description in. "I know I have but the body of a weak and feeble woman; but I have the heart of a king, and of a king of England, too." (Queen Elizabeth I)
ANADIPLOSIS: Repeats the same word, using it in a grammatically different way each time. "Some men are born with greatness , some men achieve greatness, and some men have greatness thrust upon them." - William Shakespeare
ANALOGY: Sure, all writers do it. But outlandish analogies are funny. Here's an example of analogy mixed with ALLUSION. "You would think that Colorado voters might have remembered that, like Groucho Marx apropos Doris Day, they knew Michael Bennet before he was a virgin." OR "Now we get Mrs. Obama scolding us about eating junk food like a twenty-first century Marie Antoinette: 'Don't let them eat cake!'"
ANAPHORA: Repeats words. Like anadiplosis, it uses them again and again in a grammatically similar way. "I needed a drink, I needed a lot of life insurance, I needed a vacation, I needed a home in the country. What I had was a coat, a hat and a gun" - Raymond Chandler
CHIASMUS: In which you reverse the sentence structure so that it makes sense both ways. Who better than the famous wit Samuel Johnson: "Your manuscript is both good and original; but the part that is good is not original, and the part that is original is not good - Samuel Johnson
DOUBLE-MEANING: Also known as puns. Shakespeare used this in his comedies to make sex jokes. Example from the UK Telegraph: "At American universities, people study themselves, getting a degree for navel-gazing. Sometimes literally. Now, fat people can major in 'Fat Studies.'" Groucho Marx: "I believe in computer dating, but only if the computers love each other."
EPONYM: You give something or someone a humorous and familiar name. This one also uses Chiasmus. "The unhealthiness of Dependistan isn't that it's a waste of money; it's unhealthy money that wastes people." (from the Wall Street Journal editorial page)
HYPERBOLE: Exaggeration. "This steak isn't rare; I've seen cows hurt worse than this get up and get well."
PERSONIFICATION: Martin Amis, Money: "The truth is very tactless."
WORD-ORDER MANIPULATION: From the New York Post: "They say every student has a right to a 'non-threatening learning environment. If they don't learn anything in this non-threatening learning environment, it's still better than the non-learning threatening environment of most schools."

There's a lot more, but this should get you thinking about rhetorical devices. Or devising some rhetoric to express your thoughts.