The Space Jockeys touched down on the planet to investigate it and they found the eggs. They brought them onboard when one hatched and infected one of the Jockeys. He put out the warning before he died and the resulting alien turned the rest of the crew and whatever else organic materials they had onboard into the eggs in the lower chamber where they put all the other eggs.
The giant Jockey-Alien then went outside and froze, eventually fossilizing into a hill that Dallas and co pass by on their way to the Derelict.
This is why the interior of the Derelict looks like an Alien lair, either the Jockey-Alien made it like that when it took over the ship or it got that DNA from the Jockey and passed it onto the eggs it made (since the ship looks like it was always organic).