There are several things we learn about Dillard's humorous side in An American Childhood. For one thing, she likes to play practical jokes. However, these aren't the potentially harmful type, like pulling the chair out from under someone. Instead, the jokes are generally light-hearted and harmless. For example, if someone called her and it was the wrong number, she liked to hand the phone to the nearest person and say, "Here, take this, your name is Cecile," or whoever the person was calling for.
In chapter 10, we get an idea of Dillard's mother's style and feelings when it comes to telling jokes in general. For one thing, both she and Dillard's father had a unique respect for the art of joke-telling.
"People who said, 'I can never remember jokes,' were like people who said, obliviously, "I can never remember names,' or 'I don't bathe.'... Telling a good joke well- successfully, perfectly- was the highest art."
Unlike Dillard's father, who favored meandering stories with humorous final endings, her mother
"favored a staccato, stand-up style... Fellow goes to a psychiatrist. 'You're crazy.' 'I want a second opinion!' 'You're ugly.' 'How do you get an elephant out of the theater? You can't, it's in his blood.'"
The kinds of jokes Dillard's mother liked best are a reflection of her over-all fondness for playing with language. When defining her mother's way of speaking in chapter 6, Dillard says,
"Her speech was an endlessly interesting, swerving path of old punch lines, heartfelt cris de coeur, puns new and old, dramatic true confessions, challenges, witty one-liners, wee Scotticisms, tag lines from Frank Sinatra songs, obsolete mountain nouns, and moral exhortations."
Dillard's mother's speech borrowed from many different sources, many times as a result of her thinking it sounded particularly silly or weird. She enjoyed interjecting with nonsensical phrases simply because they sounded interesting to her. For example, after hearing, "Terwilliger bunts one," on the radio, she spends years saying and writing it in various situations, none of which make sense in the context but all of which, no doubt, amuse her. The fact that puns were one of the common types of jokes she tells is another demonstration of how much her playfulness with her speech influenced her sense of humor.
In summary, one might define Dillard's mother's sense of humor as light-hearted, clever, and often heavily focused on word-play.