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Chlorofluorocarbons (or CFCs) are the most likely candidates for artificial insertion into the Martian atmosphere because of their strong effect as a greenhouse gas. This can conceivably be done relatively cheaply by sending rockets with a payload of compressed CFCs on a collision course with Mars. When the rocket crashes onto the surface it releases its payload into the atmosphere. A steady barrage of these "CFC rockets" would need to be sustained for a little more than a decade while the planet changes chemically and becomes warmer.

As the planet becomes warmer, the CO2 on the polar caps sublimes into the atmosphere and contributes to the warming effect. The tremendous air currents generated by the moving gasses would create large, sustained dust storms, which would also contribute to the warming of the planet by directly heating (through absorbing solar radiation) the molecules in the atmosphere. Eventually Mars would be warm enough that CO2 could not solidify on the poles, but liquid water would still not develop because the pressure would be too low.

After the heavy dust-storms subside, the warmer planet could conceivably be habitable to some forms of terrestrial life. Certain forms of algae and bacteria that are able to live in the Antarctic would be prime candidates. By filling a few rockets with algae spores and crashing them in the polar areas where there would still be water-ice, they could not only grow but even thrive in the no-competition, high-radiation, high CO2 environment.

If the algae are successful in propagating themselves around parts of the planet, this would have the effect of darkening the surface and reducing the albedo of the planet. By absorbing more sunlight, the ground will warm the atmosphere even more, and the atmosphere will have a new small oxygen contribution from the algae. This is still not enough oxygen for humans to breathe, but it's a step in the right direction. If the atmosphere grows denser, the atmospheric surface pressure may rise and approximate that of Earth. At first, until there is enough oxygen in the atmosphere, humans will probably need nothing more than a breathing mask and a small tank of oxygen that they carry around with them. To contribute to the oxygen content of the air, factories could be produced that reduce the metals in the soil, effectively resulting in desired crude metals and oxygen as a byproduct. Also, by bringing plants with them (along with the microbial life inherent in fertile topsoil), humans could propagate plant life on Mars, which would create a sustainable oxygen supply to the atmosphere.

and here is a nice pic of how the entire process would look like: