The funniest jokes in a performance tend to be topical to what's going on recently. For example, if someone makes a cow joke, then running on that theme or referencing a previous joke can feel more original and engaging than hearing random jokes.

To make a play on multiple meanings of a word or phrase, for example take the word calculator and break down the syllables that have dual meanings or sounds like another word(like turning the first syllable cal into cow) which leads to building a simple joke about putting cows and math together. So for example:

"How does a cow do math? With a cowculator!"

Making a reference to something obscure but hopefully well known, for example:

"Where did you learn that joke? At bovine university?"

You can build up to a punchline to throw off the audience, like starting the joke with "what do you get when" and instead of an expected pun which merges 2 things, make a straightforward answer as a twist. For example:

"What do you get when you cross a cow with an octopus? A visit from the Scientific Professional Ethics Committee and immediate withdrawal of your grant funding."

These might be too long for some rooms where shorter bits are more appreciated. They can be a longer version of a punchline twist joke which can tell a story where you build some expectation of a punchline, and deliver an unexpected conclusion. For example:

"An interviewer asks a farmer "how much milk do these cows give?" and the farmer replies "which one? The black one or the brown one?" The interviewer says "the brown one" so the farmer replies "a couple of litres per day." Then the interviewer asks "and the black one?" and the farmer replies again "a couple of litres per day."

The interviewer is naturally a bit flummoxed and says "I see. What do you give them to eat?" The farmer replies "which one? Black or brown?" The interviewer says "black." The farmer says "it eats grass." So the interviewer says "and the other one?" And the farmer again replies "grass."

The interviewer gets annoyed and says "why do you keep asking which one when the answers are the same?!" The farmer replies "because the black one’s mine." The interviewer says "oh, and the brown one?" and the farmer says "it’s also mine.""

A low effort piece of humor would be leading into a well known song by working the lyrics into a sentance, and then starting to sing it as you get a few words into the lyrics. For example:

"The other day I was making my way down town, walking fast, faces pass, and I'm home bound."