Melting Ice and Thickening the Atmosphere
Over time, the warming effect would encourage the planet to thaw out more on its own and eventually lead to the creation of a more livable atmosphere on Mars. Gravity will be a challenge — scientists are worried that Mars lacks the "pull" to keep whatever atmosphere is created.
Thawing the Pole
The Martian South pole has a coating of dry ice (which is frozen carbon dioxide), covering frozen water. As the dry ice melts, carbon dioxide could be released into the atmosphere, further accelerating the warming process.
Clouds, Rivers and Oceans
If Martian astronauts are able to accelerate plant growth and raise the temperature of the Martian atmosphere with greenhouse gasses, the theory is that buried ice will melt and seep up from underground. Some of it would vaporize and create clouds in the sky. Water vapor is actually a greenhouse gas more powerful than carbon dioxide, and again, could possibly work to raise the planet's temperature. From the new clouds, rain would fall, and the hope is that soon enough, the red dust that covers Mars would be washed away. Earth-like blue skies could appear, and rivers and oceans could return.
With its carbon dioxide-rich atmosphere, and artificially increased ammonia levels, Mars could have an ozone layer that is thick enough to filter solar radiation. This would allow future inhabitants of Mars to walk the surface without the use of protective sun shielding.