GenlyAi: Mars' mass is not too much of a problem, it could hold a higher concentration of CO2. So, first step I think, we'd need to increase CO2 in the atmosphere to increase the greenhouse effect. But for that you'd need some kind of plants or algae or bacteria that can "breath out" CO2 and that can survive with little to no liquid water (unfortunately we never seemed to prove beyond a doubt that Mars contains water) and oxygen.
Now, increasing oxygen levels would come later...
PS. I'm a professional astronomer, PhD and all, but this is completely different than my chosen field of research.
EDIT: Of course, if we were a much more advanced civilization, we could terraform ir like Earth was... bombarding it with comets full of water. :)
i_ni: Just collapse the planet a bit(~ 1/3 in size) -- any decent civ can do it...
Edit: fix number
The thin atmosphere isn't the biggest problem with trying to live on Mars. It's the lack of energy. It would literally be easier to live at the bottom of the ocean off the coast of Antarctica. It would be a lot warmer there too. The only other place worse than Mars is Venus. Anywhere but Mars and Venus, basically. Anywhere in the inner solar system would be better than Mars and Venus.
NASA recently announced the discovery of exposed sheets of very thick water ice (many meters deep) under the dusty surface of Mars. There's plenty of water, just not enough energy to warm it up and make it liquid. You would be dependent on nuclear power and solar concentrators, but because of all the dust, only the nuclear power would be reliable. The solar concentrators would probably require CONTINUOUS dust removal, and that might waste what little solar energy they are able to collect.
With a thin atmosphere and no significant magnetic field, people and agriculture will not be able to survive the radiation at the surface. So, not only are you dependent on nuclear power and solar concentrators, you also must do it UNDERGROUND. Seriously, the deep ocean beneath the Antarctic ice sheet is like a tropical paradise in comparison to the surface of Mars.
I have no idea why people want to LIVE on Mars. Science and research, sure, but living permanently on Mars? That's going to be a hard, fragile, and short life.
Changing the mass of Mars would upset the resonance balance of all the inner planets. You could accidentally cause Earth to be ejected from the solar system. That's very, very bad. Instead, increasing the density of Mars would be safer, and probably would work better, just like i_ni suggested. It's very straightforward, but not easy. The only thing you have to do is figure out how to transmute a few petatonnes of lithospheric elements like oxygen, silicon, etc into gold, platinum, and maybe something really neat like plutonium and uranium.
If it's radioactive, you get bonus heat from decay that will build-up and restart the core dynamo in a few million years, so Mars can have a powerful magnetic field to shield the surface from solar radiation.
After you achieve all that, with the huge amount of money you will make from licensing your alchemy technology, you will be able to retire on the warm and sunny beaches of Antarctica! You're going to need extra-good sunblock in the scorching -120 degree temperatures of Antarctica.
