Rito is a young boy attending high school and living with his sister. When trying to confess his love to a girl at school a ship crashes into Earth from outer space, and he somehow ends up engaged to a beautiful alien princess.
After the initial opening action of Lala's escape that the viewer or reader is treated with the scene shifts to Rito, where he is attempting to work up the guts to confess his love for Haruna Sairenji. He is then reminded of all the times he has failed before due to circumstance beyond his control. After working over his fear Rito opens his mouth to confess... and Lala's ship crashes down right on top of him, without Lala inside. Rito immediately remarks "WHY???" at the top of his lungs. At his home that night, soaking in his bathtub to wash away his sorrows he laments his fate, until Lala lands in his bathtub, completely naked.
At this point I must explain a fact about Rito, for the vast majority of both anime and manga Rito panics upon seeing a girl in somthing so simple as a swimsuit. Imagine his level of panic upon finding himself groping Lala's huge breasts.
The girl introduces herself as Lala, the princess of the planet of Deviluke, and an alien after Rito makes that remark. That very night, three men (or just Zastin in the manga) crash into Rito's room, demanding that Lala return home. When they attempt to force Lala to comply Rito, perhaps fuctioning on a random burst of courage, steals Lala away from the goons and makes a break for it across the rooftops (or lures Zastin into being hit by a train in the manga) When they are cornered Lala springs it on Rito that they have been engaged. Zastin and his henchmen bow to this and leave to "observe".
Predictably, Rito is flipping out over the "misunderstanding" and at first becomes extreamly agitated by almost anything Lala does. He predictably starts to soften towards the wayward princess because honestly, Lala is impossible to hate (really, could you resist that face? I don't think so). While at the same time his affection for Haruna remains and this worries him.
This is where anime and manga diverge.
Anime: rapid fire ecchi situations with many young girls. Lala's father comes to "test" Rito on becoming "number one in the universe". Lala's father drops the ultimatum, "get to my ship by this time or I will destroy the Earth" Rito wins and earns the right to marry Lala in her father's eyes. During the ceremony Lala exclaimes that she was being selfish and attempst to use a device to erase the memory of all involved, saying before she activates the device, "I love you Rito". Predictably, the device fails and Lala goes back to school with everything as it was.
Manga: Everything that happened in the anime plus dozens more ecchi situations and numerous pointless adventures. However, only in the manga does Lala royally (pun intended) screw up and turn Rito into a girl. Not to mention an attractive girl that Saruyama, his best friend, falls in love with.
At the climax of the manga Rito is confronted with a choice, save Lala, or save Haruna. He risks it all to save them both and almost drowns in the process. Afterwards he admits his romantic feelings directly to Lala, including his dual romantic interests in Haruna AND Lala. Lala simply shrugs it off and says, with a huge smile on her face, that once he marries her and becomes king of the universe, Earth rules will no longer apply. When he goes to tell Haruna the same thing however, Haruna has a wardrobe mishap and Rito sceams "I love you" to the entire ecchi cast, including an assassin (Golden Darkness/Yami-chan), a girl with a male alter ego (Run/Ren), his school nurse Mikado, and both of Lala's twin sisters. Lala of course thinks that Rito really meant that he loved all of them and expresses joy that they would all be able to live with each other.