The following section contains information from StarCraft: Retribution.
Arrival on Aridas
By the decree of Emperor Arcturus Mengsk, the Commander and his battalion were commissioned to aid Jenson Archimedes in search of the Argus Stone, an object of immense power located on the planet of Aridas. The object had drawn the protoss and zerg to the world as well. To ensure that the Dominion claimed the stone before its enemies, the Commander transported Archimedes and his team of scientists to a set of important ruins while fending off the zerg and protoss attacks.
Upon arrival at the ruins, Archimedes informed the commander that a cerebrate was using xel'naga technology to control a protoss tribe. Archimedes thus presented the Commander with a choice: capture the cerebrate so that Archimedes may study it at the cost of provoking a massive attack from its protoss slaves or killing the cerebrate and severing such an alliance. Ultimately, the commander made his decision.
The Crucible of War
The commander was later tasked with assaulting an Aridian space platform that had fallen to the protoss, successfully retaking the station. Afterward, the commander was assigned to retake an outpost that had fallen to the zerg in a remote region of Aridas. Not long after this, the commander was again fighting the protoss, this time re-claiming a vein of crystals that were vital to Aridian supply lines. Once again, the commander was successful.
The cycle of attack and retaliation was finally broken courtesy of a distress call by Archimedes: he'd been exploring a large cavern underneath Aridas in his ship when the zerg captured his vessel. The commander managed to rescue him.
Battle for the Argus Stone
The rescue of Archimedes was timely, considering that he'd found the Argus Stone, which was in the hands of the protoss. They'd fled to a set of reinforcements. The commander drove them back, only to find that they'd summoned a temple from Aiur designed to focus the energies of the Stone. The commander destroyed it, allowing Archimedes to successfully retrieve the Argus Stone.
Ultimately however, the Stone was lost to the zerg.