The Oppressor One, much like the Skith themselves, was composed of a type of crystal similar to ice. The ship was powered by a fusion core, and had a column of light in its centre that either contained or defined the ship's central computer intelligence, the Mindcore. Areas of the ship contained holding cells, extensive libraries, and laboratories for genetic cataloguing and experimentation. (COMIC: The First)
The Skith used the Oppressor One to visit alien planets. When they found a planet in its original state (undisturbed by other aliens), the Skith would make a detailed catalogue of the planet's species, take samples, and convert the remaining planet and denizens to Skith-self.
The Oppressor One landed on Earth in Antarctica in 1915. Its crew conducted genetic experiments on the nearby whales. Shortly after starting, they encountered the Trans-Antarctic expedition of Ernest Shackleton, whose ship, the Endurance, was trapped in the nearby ice and experimented on the ship's crew. They also soon encountered the Tenth Doctor and Martha Jones, who quickly took exception to the work the Skith were doing. The Skith Leader's interrogation of the Doctor led him to the conclusion that they were not the first visitors to Earth, making their trip there a failure. The Leader started the planetary conversion anyway.
The Doctor allowed himself to be partially converted to Skith-self and merged with the Oppressor One's Mindcore. With a little manipulation he threw the ship's drive into imbalance and then fled. The Oppressor One exploded soon after. (COMIC: The First)