It would take decades, if not centuries to even get through the first phase of terraforming mars. We would have to begin with warming the planet up. this could be done in a number of ways. For example;
- Large orbital mirrors that reflect sunlight (and thus heat) towards Mars' surface.
- Greenhouse gas production facilities to create a global warming scenario.
The mirrors would be so huge that they would have to be constructed
in space. This is possible, but not without a huge effort and a huge amount of money (which is not very likely to become available in the next decade). The project itself would also take a long time.
The mirror would be able to raise the surface temperature by several degrees. If they aim it at the polar caps, it will melt and release the CO² which is believed to exist in the ice.
As for the greenhouse gas producing facilities... i'd say we have experience in that area
this plan would give a far easier first phase but a much harder second phase; actually building stuff on mars. This would mean manned missions and material transport. A lot and often.
Ofcourse, for the atmosphere to change planet-wide, it would take centuries if not millenia. It took Earth billions of years to evolve in to a habitable planet. So, an area-specific terraforming plan would be much more favorable.
If we succeed to change the atmosphere to even resemble Earth's atmosphere is a small part of Mars (which would mean continious and perpetual terraforming for that area), it is possible to build a 'dome' and filter the outside atmosphere for use inside the dome.
But, alas, we'll all be dead by the time we get there
