There is some scientific debate over whether it would even be possible to terraform Mars, or how stable its climate would be once terraformed. It is possible that over geological timescales - tens or hundreds of millions of years—Mars could lose its water and atmosphere again, possibly to the same processes that reduced it to its current state.
Indeed, it is thought that Mars once did have a relatively Earth-like environment early in its history, with a thicker atmosphere and abundant water that was lost over the course of hundreds of millions of years. The exact mechanism of this loss is still unclear, though several mechanisms have been proposed. The lack of a magnetosphere surrounding Mars may have allowed the solar wind to erode the atmosphere, the relatively low gravity of Mars helping to accelerate the loss of lighter gases to space. The lack of plate tectonics on Mars is another possibility, preventing the recycling of gases locked up in sediments back into the atmosphere. The lack of magnetic field and geologic activity may both be a result of Mars' smaller size allowing its interior to cool more quickly than Earth's, though the details of such processes are still unrealized. However, none of these processes are likely to be significant over the typical lifespan of most animal species, or even on the timescale of human civilization, and the slow loss of atmosphere could possibly be counteracted with ongoing low-level artificial terraforming activities.
Terraforming Mars would entail two major interlaced changes: building the atmosphere and heating it. Since a thicker atmosphere of carbon dioxide and/or some other greenhouse gases would trap incoming solar radiation the two processes would augment one another.
Mirrors made of extremely thin aluminized Mylar could be placed in orbit around Mars to increase the total insolation it receives. This would increase the planet's temperature directly, and also vaporize water and carbon dioxide to increase the planet's greenhouse effect.
While producing halocarbons on Mars would contribute to adding mass to the atmosphere, their primary function would be to trap incoming solar radiation. Halocarbons (such as CFCs and PFCs) are powerful greenhouse gases, and are stable for lengthy periods of time in atmospheres. They could be produced by genetically engineered aerobic bacteria or by mechanical contraptions scattered across the planet's surface.
Changing the albedo of the Martian surface would also make more efficient use of incoming sunlight. Altering the color of the surface with dark dust, soot, dark microbial life forms or lichens would transfer a larger amount of incoming solar radiation to the surface as heat before it is reflected off into space again. Using life forms is particularly attractive since they could propagate themselves.
Nuclear bombardment of the crust and the polar caps has been suggested as a quick-and-dirty way of heating up the planet. If detonated on the polar regions, the intense heat would melt vast quantities of water and frozen carbon dioxide. The gases produced would thicken the atmosphere and contribute to the greenhouse effect. Additionally, the dust kicked up by a nuclear explosion would fall on the ice and decrease its albedo thus allowing it to melt faster under the sun’s rays. Detonation of nuclear weapons under the surface would heat the crust and help speed outgassing of trapped carbon dioxide. While using nuclear devices is attractive in the sense that it makes use of ageing and dangerous Earth weaponry and adds quick and cheap heat to the planet, it carries the ugly connotations of mass destruction to the native environment and potential harmful effects of nuclear fallout.
Another possibility to heat the surface of Mars would be to place a microwave array, powered by solar cells, nuclear reactor, or a combination of the two, into geosynchronous orbit. Microwaves of approximately 2.45GHz are used in microwave ovens to cause vibrations in water molecules and produce heat. If microwaves of this frequency with sufficient amplitude were focused onto the surface of Mars it would heat the ice crystals trapped in the soil. A long enough exposure to the microwaves would release the water into the atmosphere and gradually heat the surface of the planet. Several such arrays could be placed in orbit around Mars and designed to gradually sweep the beam across vast areas.
One drastic proposal for adding some heat to Mars is to brake the inner moon, Phobos, so that it crashes into the surface. Apart from the comparatively little heat generated by this, it removes an important danger for future settlements: A thickening atmosphere would slow down Phobos so much, that it would crash land within a few hundred years anyway.
Thinking far into the future, some scientists point out that the Sun will eventually grow too hot for Earth to sustain life, even before it becomes a red giant star. All main sequence stars brighten slowly throughout their main sequence lifetimes. As a result, Mars will warm up on it's own, making terraforming easier.
Since ammonia is a powerful greenhouse gas, and it is possible that nature has stockpiled large amounts of it in frozen form on asteroidal sized objects orbiting in the outer solar system, it may be possible to move these and send them into Mars' atmosphere. Since ammonia is NH3 it would also take care of the problem involved in needing a buffer gas in the atmosphere. Impacting a comet onto the surface of the planet might cause destruction to the point of being counter-productive. Aerobraking, if an option, would allow a comet's frozen mass to outgas and become part of the atmosphere through which it would travel. It may be better to impact several smaller asteroids into the planet, both to build up the planet mass and to add to the atmosphere. Keeping these smaller impacts on their own will eventually build up the temperature as well as mass to both the planet and its atmosphere.
The need for a buffer gas is a challenge that will face any potential atmosphere builders. On Earth, nitrogen is the primary atmospheric component making up 77% of the atmosphere. Mars would require a similar buffer gas component although not necessarily as much. Still, obtaining significant quantities of nitrogen, argon or some other non-volatile gas could prove difficult.
Hydrogen importation could also be done for atmospheric and hydrospheric engineering. Depending on the level of carbon dioxide in the atmosphere, importation and reaction of hydrogen would produce heat, water and graphite via the Bosch reaction. Adding water and heat to the environment will be key to making the dry, cold world suitable for Earth life. Alternatively, reacting hydrogen with the carbon dioxide atmosphere via the Sabatier reaction would yield methane and water. The methane could be vented into the atmosphere where it would act to compound the greenhouse effect. Presumably, hydrogen could be gotten in bulk from the gas giants or refined from hydrogen-rich compounds in other outer solar system objects, though the energy required to transport large quantities would be great.
Simply thickening the Martian atmosphere will not make it habitable for Earth life unless it contains the proper mix of gases. Achieving a suitable mixture of buffer gas, oxygen, carbon dioxide, water vapor and trace gases will entail either direct processing of the atmosphere or altering it by means of plant life and other organisms. Genetic engineering would allow such organisms to process the atmosphere more efficiently and survive in the otherwise hostile environment.
Another significant, and probably most over-looked aspect of terraforming Mars, would be the lack of a magnetosphere. The magnetosphere deflects most of the hard particulate radiation from the solar wind. Without some form of radiation protection anyone on Mars would have prolonged exposure to an unhealthy amount of radiation every time a serious solar eruption occurred. Terraforming involves making life viable on another world, and so long as that life is going to be exposed to high levels of radiation it will not be desirable. The lack of a magnetosphere is also thought to have contributed to the lack of Martian atmosphere in the first place, the solar wind adding a significant amount of heating to the atmosphere's top layers. Venus, however, shows that the lack of a magnetosphere does not preclude an atmosphere. A thick atmosphere will also provide radiation protection for the surface, as it does at Earth's polar regions where aurorae form, so in the short term the lack of a magnetosphere would not seriously impact the habitability of a terraformed Mars.
On a longer timescale, and with the technology of the future (in perhaps 25-50 years), an artificial magnetosphere seems possible: If the energy of several large fusion-power-stations is used to power large superconducting magnets - the field should be strong enough to protect at least local settlements.
