The movie opens beautifully with Jerry Travers (Astaire) trying to silently fold his paper in a "silent" club while waiting for Horace Hardwick (Edward Everett Horton), the producer of a show in which he's about to star. Horace sets Jerry up staying with him in his hotel and then tells Jerry that he wants Jerry to fly to Italy with him after the show to meet up with his wife Madge (Helen Broderick) and some girl Madge wants to fix Jerry up with. Jerry doesn't really want to go.
Jerry: "Is she expecting me for a weekend or a wedding?"
Horace: "You know how wives are...
Jerry: "No I don't. How are they?"
Jerry especially doesn't want to go anywhere after he meets the beautiful Dale Tremont (Ginger Rogers), another hotel guest. Jerry meets Dale when he tap dances in the room above her while she's trying to sleep, and she has to come upstairs and give him a piece of her mind. Jerry tells Dale that she can help cure him of the dancing with a good hug, to which she replies, "Well I'll call the house detective and tell him to put his arms around you." I'm choosing to think of the whole thing as a meet cute... Jerry woos Dale with flowers and then by paying off a handsome cab driver to give him the cab so that Jerry can drive Dale to the stables the next day. Dale discovers Jerry is her driver only when he starts to tap dance above her.
Dale starts to fall for Jerry at the stables when he dances with her in the rain.
Jerry: "May I rescue you?"
Dale: "...I prefer being in distress."
The thunder drives Dale to seek out Jerry for comfort in the gazebo in which they are both waiting out the storm, and pretty soon they are dancing and in love.
Happiness leads to mistaken identity and anger, though, when it turns out that Dale is Madge's friend. And Dale, never having met Madge's husband, thinks that Jerry is really Horace. She is suddenly horrified by his advances, slaps him, and gives him the motivation he needs to fly off to Italy to continue to woo her. He has no idea what he did to make her so mad.
The rest of the movie is all about mistaken identity and is, in my opinion, hilarious.
Dale tells Madge that Madge's husband is chasing her:
"Really, I didn't know he was capable of that much activity... Did he catch you?"
Jerry wants to propose to the still confused Dale:
"Alright, you go find all about her past, and I'll go find out about her future."
Jerry and Dale dance with a crazy dress Dale is being payed to model: