Once upon a time (before the film starts) Hildy Johnson was the star reporter of the Morning Post and the wife of its editor, Walter Burns.
But then Hildy realized that Burns was a "stinker" (that's 1940's for "dirtbag"), divorced him, quite her job, left town, and got engaged to nice-guy insurance salesman Bruce Baldwin… who treats her like "a woman" instead of "a water buffalo." And they lived happily ever after.
Or they would have, except that fate and some pretty explosive chemistry intervenes. Hildy stops back in at the office (Bruce in tow) to tell Walter she's leaving for Albany to get re-married. Walter doesn't like that at all; he's determined to get Hildy back (the stinker).
Walter has another problem too. Earl Williams, a bookkeeper, is due to be executed for shooting an African-American policeman. The black voters in the city hold the power to sway the upcoming election, so the Sheriff and the Mayor have decided to execute Williams even though he's not in his right mind.
Walter wants to save Williams, embarrass the mayor, sell papers, and get back Hildy… not necessarily in that order. So, he offers to take out a big fat insurance policy from Bruce if Hildy will write him a story that makes Earl Williams look innocent. Hildy agrees. And her fate is sealed.
At the prison, Hildy is embroiled in an escalating series of scoops. First Earl Williams escapes. Then he climbs into the pressroom where Hildy is alone, and she hides him in a rolltop desk. Then Molly Malone, Earl's friend, throws herself from a window after being tormented by the press dudes, who really are stinkers, too. ("They ain't human!" Molly declares. "They're newspapermen," Hildy replies wearily.)
While all this is going on, Hildy keeps trying to write her story and leave. But she can't quite pull herself away, in part because she loves the newspaper business, and in part because Walter keeps plotting against her. He arranges it so that Bruce goes to jail over and over (once by planting a watch on him; once by sending a woman to solicit him). He even has Bruce's mother kidnapped. (Your mother-in-law isn't likely to forgive you when your ex-husband has her kidnapped. Sad truth.)
Finally, Walter shows up at the pressroom in person to try to help Hildy remove the desk in which Earl Williams is hiding. Bruce comes back too, finally out of jail, and insists that Hildy go away with him immediately—but she's too excited by the prospect of writing her awesome exposé, and he ends up leaving without her.
Before Walter and Hildy can take the desk out they're discovered by the Mayor and the Sheriff, who arrest them for obstruction of justice. All seems lost—but suddenly a messenger (named Pettibone) shows up from the governor saying the Earl Williams is pardoned.
Walter and Hildy question the messenger and find out that he'd come earlier, and the Mayor had tried to bribe him not to deliver the pardon. So now Walter has his big scoop, and the Mayor and the Sheriff are in deep doo-doo (that's the technical legal phrase).
Hildy is about to leave to try to catch Bruce, when she and Walter find out that the wayward fiancée has been arrested again, this time for trying to pass counterfeit money Walter set him up with. Defeated, Hildy realizes she still loves Walter, and they agree to get remarried and honeymoon at Niagara Falls—or possibly in Albany, since at the last minute Walter discovers there's an important strike happening there.
You might get the girl at the end, but you're still a stinker, Walter.