The year is 1965 and Sam is a twelve-year-old orphan in foster care, living on an island. He falls in love with the equally troubled Suzy and they run away together. Sam's Khaki Scout troop leader Scout Master Ward (Edward Norton) leads Sam's fellow scouts in the search, joined by Suzy's parents (Frances McDormand and Bill Murray) and Coast Guard Captain Sharp (Bruce Willis). Seeing them together makes Suzy's father realize that his wife is having an affair with Sharp, which Suzy already knew.
Sam and Suzy are eventually found and Suzy is returned home. Her mother ends her affair with Sharp. Sam's foster parents refuse to take him back and Social Services tells Sharp and Ward that based on his history Sam will be placed in "juvenile detention" and may be given shock therapy, to their distress. Sam is placed in Sharp's care until Social Services comes to get him. Sam's fellow scouts decide that they've been unfair to Sam and help him and Suzy escape again. This involves going to Fort Lebanon where a regional meeting of the Khaki Scouts is being held to get assistance from one of the scouts there, who marries Suzy and Sam at their insistence.
They're discovered by the larger group of Khaki Scouts who set off in pursuit, eventually joined by Ward, Sharp and Suzy's parents. A hurricane hits the island and everyone goes to the church where Sam and Suzy met and are hiding, as it's the local hurricane shelter. Social Services shows up to take custody of Sam. Sam and Suzy climb onto the church tower and prepare to jump into the floodwater below to escape. With help from Suzy's lawyer parents, Sharp convinces Social Services to let him foster Sam and he joins them on the church tower and offers to be Sam's foster father. Sam and Suzy agree and take his hand just as the church tower collapses, and Sharp saves them.
The film ends with Sam visiting Suzy at her parents' house, with Sharp waiting to take him home.