The first task: heating up Mars.

The best approach is to increase the effectiveness of solar heating by trapping IR radiation that the surface of Mars re-radiates into space. Need molecules in the atmosphere that are highly opaque to IR light: "super-greenhouse" gases (perfluorocarbons "PFCs" such as CF₄, C₂F₆, SF₆ that can be manufactured from Martian materials).

A few parts per million of super-greenhouse gases would increase the average temperature by 36^oF. This thaws CO₂ in the polar caps, adding CO₂ to the atmosphere which is another greenhouse gas. This leads to further heating ... eventually producing a thick, warm atmosphere in about 100 years.