Sir Evil accomplished this by somehow gaining control over the energy inside Mars, then releasing it en masse through the blue crystals. The crystals, designed only to slowly disperse the energy into the air, were unable to handle this energy and released it. As a result, nuclear explosions took place across the surface of the planet, transforming it into a barren wasteland.
While the effects of the Martian Winter were devastating, Sir Evil was only partly successful. Under normal circumstances, the energy release would have destroyed the entire planet. But one crystal, which later became known as the Crystal of Eyefourgott, malfunctioned and stored much of the energy, essentially saving the planet from even greater disaster. Both Malvadon and the Last Brigade were able to infer the crystal's existence, but it wasn't located until thousands of years later by Marvin the Martian.
It should be noted that this event had nothing to do with the eventual destruction and recreation of Mars at the hands of Dokuma.