As the human population of earth grows and our climate begins to decay, we will need to look elsewhere in our solar system for places to live. The most likely planet orbiting our sun for human colonization is mars. It's atmosphere, gravity, and rotation most closely matches that of the earth. Mars, however, is not currently habitable. The average temperature of the planet is -81 degrees Fahrenheit (-62.77 degrees Celsius) and what little atmosphere it has is composed of 95.3% CO2. Due to this, Mars would have to be terraformed before it became a viable place for us to live. What exactly is terraforming? Terraforming is the process by which we might make a planet close enough to Earth that terrestrial life could exist there.
Mars is even more appealing for terraforming because it has large stores of frozen CO2 which could be released to cause a green house effect on the planet to warm it up. If enough CO2 could be released, it would cause a chain reaction and release the rest of the stored CO2, warming the planet up enough where basic microbial life and plants could begin to change the CO2 into oxygen and create an atmosphere suited to human life. One big problem with a Martian atmosphere is the absence of a "buffer" gas. On earth, the somewhat inert gas nitrogen acts as a buffer and makes complex life possible, but there is no such gas on mars. We might have to transport a buffer gas from earth or from frozen deposits in other celestial bodies to make a breathable atmosphere on mars, and this could be very costly.
The first step in terraforming mars is raising its temperature. Once we give the planet a large enough push, we might see the before mentioned chain reaction with the green house effect. The problem we see then is how to start this reaction. Several solutions have been proposed. One of the more costly of which would be to put large pumps on the planets surface to constantly pump CO2 into the atmosphere. This option is elegant, but not very economical. More practical solutions have been proposed however, such as smashing ammonia rich asteroids into the planets surface to create the initial collision temperature and to accelerate the green house effect using ammonia as an effective greenhouse gas. Other options involve rockets sent from earth. If we were to bomb the polar ice cap of mars, we could release enough CO2 to start the chain reaction. The explosion would have to be rather large however, on the scale of a hydrogen bomb. Or we could sent a series of rockets containing compressed chlorofluorocarbons to Mars over the course of a decade. It has even been suggested that we place a giant mirror in orbit around Mars to reflect more sunlight at the planet to increase it's temperature.
Other problems crop up with terraforming mars aside from just it's atmospheric composition. Mars doesn't have a magnetic field to shield it like the earth does, which means that any life that should arise on its surface would be subject to solar rays and high amounts of radiation. The lack of a magnetic field also means that solar radiation would slowly blast away any atmosphere that we tried to put on the planet.
Regardless of all of these problems, humans are destined to grow beyond the bounds of the earth, and mars is the best planet for us to grow to. There is no problem that cannot be overcome with a little ingenuity.