How could we accomplish this?
The sunlight that hits a planet's surface arrives primarily as visible and ultraviolet light. The planet absorbs this solar energy, and then radiates warming infrared energy back out into the atmosphere. Greenhouse gases in the atmosphere work as a global layer of insulation, trapping that infrared radiation and preventing it from escaping into space.
But, how could we accomplish this? In the 1970's, astronomer Carl Sagan suggested covering the polar caps with dark material - such as carbon black from a pulverized asteroid - to a depth of 1 millimeter. Sagan estimated that over 100 million tons (or a 600-meter asteroid) would be necessary to cover the ice caps. This cover would have to be replaced each year due to frequent dust storms. Since this would be a very arduous task, Sagan also proposed using plants that are capable of growing on ice.
In the 1980's, Planetary scientist Chris McKay suggested that we could seed the Martian polar caps with green plants or genetically engineered microbes that extract the liquid water they need from ice. These organisms would be dark and, thus, would absorb more sunlight that would warm up the ice and increase the overall rate of evaporation. If the surface temperature was high enough, more carbon dioxide might be released from the Martian soil, permafrost, and polar ice and would flood the lowlands. This process could take from 100 to 10,000 years.
The benefit of using plants or microbes is that they are self-reproducing. Research has shown that some microbes can survive in a simulated Martian environment, similar to Earth's polar regions. Such organisms could spread out over the ice caps in a relatively short time. This process would take a few hundred years to free the ancient atmosphere of Mars. The increased surface pressure and temperature would then allow liquid water to condense on Mars. There would be rain, rivers, and perhaps even oceans. Other green plants would grow on Mars, getting nutrients from the soil and carbon dioxide from the air just as they do here on the Earth.
Edited: Images of the "Tharsis" and "Hellas" hemispheres of a terraformed Mars, rendered as if viewed from the altitude of Deimos's orbit. Created by Darren Glidden using MOLA data manipulated in Adobe Photoshop.
I follow those who I will someday lead. - Candy