Most current evidence points to the theory that billions of years ago, Mars was a warm and wet planet. Orbiting probes have sent back images showing water-carved features on Mars, such as canyons and river valleys. Yet today, Mars is a dry, desert-like world mostly devoid of water and with a thin atmosphere of mostly carbon dioxide.
Although no evidence of life has yet been found on Mars, the planet contains all of the chemical elements needed for life. So could Mars's environment be changed, so that it would be more hospitable for colonization by Earth-based organisms, including human beings?
Utilizing only the technology of today, the effort could be done. The first step would be to thicken significantly Mars's carbon dioxide atmosphere. While human beings cannot breathe carbon dioxide, plants can. A thicker atmosphere would also allow humans to walk around on the surface unprotected, only using a breathing apparatus to survive.
This could be done by heating up the planet, by directing more of the Sun's energy toward the surface. It could be done by building large mirrors in orbit, to reflect the sunlight downward onto the surface. Most of the carbon on Mars is tied up in rocks, and heating the surface would cause those rocks to outgas, thickening the atmosphere. Another way to turn up the heat would be to introduce super-greenhouse gases, the same CFCs and other chemicals that have largely been outlawed on the Earth. They would provide an artificial layer in the atmosphere which could begin a greenhouse effect on Mars.
After the carbon dioxide atmosphere has been thickened significantly, the next step would be to utilize the process of photosynthesis, by introducing simple plantlife to Mars. Plants like lichens and blue-green algae could breathe in the carbox dioxide and breathe out the most important gas for humans, oxygen.
It may take hundreds of years to terraform Mars, and new methods not even dreamt of yet could be the way it is done. Yet, the transformation of Mars to an Earth-like world will be a monumental accomplishment, and would to teach us more about our own home planet, as well as teach us how to create habitable planets -- a skill that may be useful over the next several thousands of years.