The Process

 

In order to transform Mars into a planet we could successfully inhabit, we would need to modify the atmosphere to get rid of the carbon dioxide and replace it with nitrogen and oxygen. The first step in this process would be to melt the southern polar ice cap, releasing massive amounts of carbon dioxide into the air. By doing this, the greenhouse effect could heat up the planet. A subsequent introduction of plant life that could survive on mars would begin the process of photosynthesis to create oxygen from carbon dioxide. It would take a certain variety of plants to succeed at this process, because of Mars' climate and soil conditions; genetic modification of plant-life may be necessary.
It is thought that a layer of water exists underneath the southern polar ice cap:

Next problem: how to heat up the planet.

It is believed that Mars was much once warmer than it is now. The challenge lies in reattaining that higher temperature.

There are several ways that have been thought of to heat the surface and melt the southern ice caps. Some of them are more efficient than others, but all should be taken into account. One idea is to increase the amount of sunlight that reaches Mars. This could be done through the use of huge mirrors stationed in Mars' atmosphere; this plan may be difficult to attain because of the difficulty in producing a mirror 125 km in size and transporting it (even piece be piece) through space. I don't think this is the best idea. There are, however bacteria that produce either methane and oxygen with water and carbon dioxide, or ammonia and oxygen with water and nitrogen. Both methane and ammonia are strong greenhouse gases, stronger than carbon dioxide, and could produce a temperature rise of 10K in 30 years time.

http://www.nineplanets.org/mars.html
Once we have heated the planet, and made it possible for humans to breathe, what comes next?