According to the season 1 DVD release of the show, the episode "Everybody Hates the Babysitter" on the disc has the cast commentary in the episode and said that Tichina Arnold ad-libbed a lot of the things she says in the show.
Chris Rock's real family had mom, dad, 6 other brother, 1 other sister, and himself. He said that using 6 brothers and 1 sister would've been weird, so he thought it'd be better to use some of his sibling's personalities to make 2 siblings for the show.
Tichina Arnold composed a theme song for the show and recorded it with 2 of her friends. However, Ali LeRoi and Chris Rock already had some themes in mind, so they kept the ending of it to put in at the end of episodes and before commercial breaks.
Chris Rock actually grew up mostly in the 1970s instead of the 1980s. But Rock felt that 70s culture has been parodied enough with shows like That '70s Show (1998) and moved the time period to the 80s.
Rock initially did not want to cast Tyler James Williams as Chris because he felt Williams was too good-looking to play a kid that everybody hates. But CBS executive Leslie Moonves (CBS owned UPN) insisted on Williams.
Jacqueline Mazarella's role of Ms. Morello was originally only supposed to be for one episode and she had only one line. ("Hello, Chris.") But during her audition, she was encouraged to improvise and "flirt" with Chris. She impressed the producers so much that her role was expanded in later episodes.