In the film alien, how did the planet they were on become over run with aliens?
In the original movie Alien, the moon that they landed on, known as LV-426, was not actually overrun with aliens. A spacecraft piloted by another unknown alien species similar to humans crashed on LV-426. This occurred because the harmful aliens, known as Xenomorphs, took over the ship. But in the story of the film, this infestation was contained within the spacecraft and no adult aliens were present by the time the crew of the Nostromo arrived. The crew of the Nostromo then inadvertently brought a Xenomorph on board their ship when one infected one of the members of their crew.
In Aliens, a colony was established on the same moon about 37 years later using an atmospheric processor. 20 years after its establishment, the colony became overrun with aliens when a family went to investigate the same spacecraft from Alien. Though no adult aliens were originally present, the eggs were still alive and active. The family had "facehuggers" attach to their faces, which then laid eggs inside them, which later hatched into aliens. The aliens would burst from the person's body, killing them. After this happened many times, the colony was overrun by aliens. Even then, it was mostly just the colony that was overrun rather than the whole moon.
In the new prequel to Alien, titled Prometheus, a crew lands on another moon in the same solar system as LV-426.