According to Jim Recap: Getting to Know You
Cheryl gets jealous when she realizes that other men give their wives jewelry (okay, one specific man, though he's not seen) and Jim doesn't give her anything. Jim counters by saying that the only time men give women anything expensive like that is if they are trying to get them into bed, or if they are cheating on their wives. Once they're "in place", like she is, they don't need that sort of thing. Cheryl doesn't believe him (and she doesn't like the implication of what he says), and that means Jim needs to do something.
He and Andy head to the mall to buy something, and he gets her some nice earrings. When Cheryl opens them, she says that they are "wonderful", which means that she doesn't like them much, and when Jim presses her about them, she explains that they are just like the ones she has worn for the last fifteen years, and he doesn't know her very well.
When he presses her on this, she asks about her major, which he says is biology (it is business administration), her favorite band, which he says is one of those obscure bands (it is the Beatles) and her eyes, which he says are 34C. He's not doing too well. When he says she doesn't know him, she explains a little better.
She knows that his favorite movies are Ice Station Zebra, followed by A Fistful of Dollars and Pootie Tang (surprisingly, not a porno). He is afraid of spiders, gets a foot rash in the summer, likes to dance to Brick House, his mother's middle name is Madeline, he is allergic to MSG and he bites his lip when he is wrong (incidentally, he doesn't bite his lip here). I guess she does know him.
For the next few days, Jim becomes an entirely new person, devoting himself to recognizing things that Cheryl wants, and making sure she gets it. The only problem surfaces when that other guy gets caught cheating. It gets worse when she doesn't tell Jim about it, because she is enjoying all the attention. Eventually, however, the guys in the band tell Jim what happened, and Jim lets Cheryl know that she's busted for trying to put one over on him.
He says she has two options - he can take the earrings back, or he can have an affair with his secretary. Since he only works with Andy, he decides that he'll take the earrings back. But instead of just getting the money for them, he buys a pink bicycle that Cheryl told him about on their second date. How's that for knowing her?
