Anna Brady plans to travel to Dublin, Ireland, to propose to her boyfriend Jeremy on February 29, leap day, because, according to Irish tradition, a man who receives a marriage proposal on a leap day must accept it. While mid-flight to Dublin, there is a storm and the plane diverts to Cardiff, Wales. Anna hires a boat to take her to Cork, but the severity of the storm forces her to be put ashore on the Dingle Peninsula. She enlists the help of a surly Irish innkeeper, Declan O'Callaghan, to taxi her across the country to Dublin to pull off the proposal in time, and begins to question her intentions with Jeremy when she makes a connection with Declan.
At first, Declan refuses to drive Anna to Dublin, but after his pub is threatened with foreclosure the next morning, he agrees to drive her for €500. Before they leave, Declan gets frustrated at Anna's luggage and she snaps at him telling him to be careful due to the fact that her boyfriend gave it to her and it is Louis Vuitton. The two set out in Declan's rickety car, but they quickly run into a herd of cows. Anna shoos them away but steps in cow dung, causing her to lean against the car, which wheels back into a lake. Angry at Declan, Anna walks away from him; she stops a car for a lift and after offering to take her bag they drive away with her luggage to the delight of Declan.
The two eventually reach a pub where they discover the men going through Anna's luggage. Declan punches them, and they are both kicked out by the landlord. They eventually reach a railway station by foot. While passing time waiting for the train at a nearby castle, Declan asks Anna what she would save if her apartment caught fire, and she is unable to answer. The train arrives early, and Anna misses it. The two go to a bed and breakfast, where they are forced to pretend that they are married so that their conservative hosts will allow them to stay. Asked their married name, they simultaneously answer 'Brady' and 'O'Callaghan', quickly amending that to 'O'Brady-Callaghan'. During dinner, Anna and Declan are forced to kiss, which causes some confusion for them. That night, they hesitantly sleep in the same bed. The next day, they take shelter from a hail storm in a church where a wedding is taking place.
The next day they arrive by bus in Dublin. On the way to the hotel, they stop by a park and Declan reveals that he was once engaged but that his ex-fiancée ran off with his best friend and his family ring to Dublin; Anna encourages him to get his ring back. When Anna reaches Jeremy's hotel, he proposes to her, and she accepts after a hesitation as Declan walks away. At their engagement party, Anna finds out that Jeremy proposed to her only in an effort to impress the manager of the expensive condominium the two were attempting to buy.
Dismayed, Anna pulls the fire alarm and watches as Jeremy grabs all the electronics before fleeing. Anna goes back to the Dingle Peninsula in County Kerry, where Declan is successfully running his inn. She proposes that they get together and 'not make plans', and Declan leaves the room. Anna interprets this as a rejection, so she rushes outside and ends up on a cliff overlooking the sea. Declan follows her and asks, 'Mrs. O'Brady-Callaghan, where the hell are you going?' and proposes to her with the ring he retrieved from his ex-fiancée while in Dublin. Some time later, the two are shown driving in Declan's car with a 'Just married' sign in the back window.