Aeneas, a valiant Trojan warrior, flees Troy after its fall. In his last adventure in Vergil's Aenead, Aeneas meets his dead father, Anchises, in the underworld. Aeneas takes his dad's advice and settles down in Latium. There Aeneas marries the daughter of the local king. That provokes a battle with her former boyfriend, and when the dust settles, only Aeneas, among the leaders, is still standing. From the survivors he creates the new Latin tribes. Aeneas' son, Iulus Ascanius, founds a city at Alba Longa (now Castel Gandolfo) and starts a dynasty.
Three hundred years later, in the eighth century BC, Prince Amulius, deposes his older brother, King Numitor of Alba Longa, and, after killing Numitor's male children, forces Numitor's daughter, Rhea Silvia, to become a Vestal Virgin. Rhea Silvia has a liaison with Mars that results in the birth of Romulus and Remus. Amulius finds out about the birth of the twins and orders them to be slain. Instead of killing the boys, Amulius' servants hide them in a basket on the riverbank near the Tiber, where Rome now stands. A wolf finds the twins, suckles them, and takes them to her cave (the Lupercalia). A shepherd later takes them and raises them as his sons. The twins grow up, kill Amulius, and restore Numitor to the throne in Alba Longa.
They decide to found their own new city on the Tiber. Augury to determine who should be king yields ambiguous results: first Remus sees six vultures from the Aventine hill, then Romulus sees twelve from the Palatine. Remus claims he should be king because his vultures appeared first. Romulus says he has more vultures, so he should be king. There are several versions of what happens next, but they all finish with Remus dead and with Romulus as the sole ruler, the first of Rome's seven kings.
Romulus recruits local outcasts and bandits, but they are short of women so they trick a local Latin tribe, the Sabines, into a joint celebration. When the Sabine men get drunk, the Roman men seize and carry off their virgin daughters and quickly rape them all so that nobody else would want them. The daughters, according to (male) Roman historians, were women of their time and loved this kind of treatment. They send messages to whichever of their relatives survived the party, saying that they do not want to be rescued from the virile Romans. Peace is eventually restored, and Rome is on its expansive way.
Behind the myths: There is no independent evidence that Aeneas ever reached the shores of Latium (or that he ever existed, for that matter). This story gave the Romans a noble history. They couldn't prove descent from the Greeks, so why not be Trojans? Romulus and Remus, if they ever existed, were really probably Etruscan outlaws encamped on adjacent hills near the Tiber on the Etruscan-Latin border. They each had a group of followers -- they were evenly matched and alike as twins.
The story of the abduction and rape of the Sabine women could explain how the agglomeration of multiethnic outlaws on the Capitoline hill becomes part of the Latin language group: the Sabine moms raised their kids in the Latin culture.
One version of the myth of how Remus was killed says that the fight with his brother began when Remus mockingly jumped back and forth across the sacred city boundary (the Pomerium) that Romulus had plowed on the Palatine. This story of punishment for impiously crossing the city boundary was very popular with the Senate, and later, with the Pompey faction, when Julius Caesar was coming toward the city after crossing the Rubicon. The Liberatori also promoted it after they killed Julius Caesar on the Ides of March. Julius Caesar, of course, claimed to be a descendant of that Iulus Ascanius, the son of Aeneas who founded Alba Longa. Rumon was the Etruscan name of the Tiber River.
Vergil's Aenead: http://classics.mit.edu/Virgil/aeneid.html
Aeneas leaving Troy: http://www.geocities.com/Vienna/Choir/4792/aeneas.html