I assume that you, like most writers, are one single individual with a limited experince of the world. You have never murdered anyone, you don't really remember how you felt as a child, and you don't score 160 in an IQ test, yet you write about murderers, children, or brilliant scientist.
It is, of course, impossible for you to know how these people think or feel. So how can you write about them?
You fake them.
Psychology has found that people can usually judge another person's intelligence pretty accurately just from seeing that person. They don't have the person perform an IQ test, they just look at cues like facial features and signals of education and expertise like dress style and accessories (glasses, laptop case), academic degrees, who that person associates with and how he interacts and moves.
It is generally assumed that intelligent persons are successful in all aspects of life, good looking, socially competent etc. Of course this is not true (or at least not in such a simple correlation), but that are the cues that we use to judge a person's intelligence. Wit, of course, is partly intelligence, partly social competence, and partly humor. So markers for intelligence will give a clue about wit also.
Movie creators use these markers and carefully select the dress, car, and furniture of their characters. Some movie characters appear intelligent on first impression, because of what they look like and where we first see them (e.g. the lab).
A German theatre director went even further. He wrote the character's IQ on their forehead.
Of course you cannot do this in a novel, but you can do something similar: just state that they are witty, or have one character say it about another. If you don't want to be so direct, equip your character with cues of wittiness: people laughing with him or her, and if you cannot show interaction, use the other cues I mentioned above.
But let's assume that you are a witty person yourself, and you don't have to fake your character's wit. There is a danger with this. Unlike intelligence, where we all can agreee that a person winning the nobel prize cannot be stupid, wit is a question of personal taste. What I will find intelligently funny, you might think inane. It is also a question of context, current emotional state, and (sub)culture. Since you cannot control who reads your book, you run the danger of your readers finding your witty character's wit rather crude. If you tell and don't show, this won't happen.
I always say: Do not describe your characters. If the protagonist falls in love with that person, the reader will imagine that person to be beautiful after the model of his own taste. If you give the love interest a specific appearance, chances are that your reader finds that look unattractive and won't be able to follow your protagonist.
Do the same with all things that vary among your readers. Tell your readers of the effect that a character has, but
leave it up to the reader to imagine the kind of person that would cause such an effect.