I always loved this concept. There are many, many, ways we could do this.
http://en.wikipedia.org/wiki/Terraforming_of_Mars is a wiki page of terraforming Mars.
After reading this (you really don't have to) I'd like you to post your believed concept of achieving this, posted on wiki or not.
I believe we could get multiple mirrors, put them around the planet, and direct the sun's rays on them. Then, once the temp is raised a bit, the dry ice would turn to gas and the CO2 would heat up the planet.
Then, if there is some type of chemical to remove oxygen from the rust in the soil, we could use that oxygen to put animals, and a few humans on it.(We'd have to frequently fly back to Earth so our bones don't get messed up though) In addition to that, we would have a nice supply of iron to get a nice colony started.
I don't think any of those are feasible, I mean theoretically sure, but you talking on the scale of a planet. Just getting enough resources to do any one of those is a challenge. If you can heat up the planet enough for the CO2 to stay as a gas, who's to say it will stay on the planet. Mars doesn't really have an atmosphere, infact the only planet in our solar system that has an atmosphere as dense or denser than Earth is Saturn's moon Titan. How are you going to stop Mars from heating up once it reaches the optimal temperature ? Kind of a problem we are facing now, or at least people are arguing whether global warming even exists.
...we'd wait about 20 years for the radiation to get to a safe level...
Wut? Where'd you get this magic number 20? Have you heard what happened to Japan and Chernobyl? I might be talking out of my ass here, but I don't think nuclear bombs is a wise way to heat up Mars. Besides, you'd have to fire off so many bombs continuously, which would break every single nation economically and resource-wise.
Oh, and the astronomer I mentioned in my previous post brought up the idea of heating up Mars by reflecting light off satellites (that's why he said 50+ years).
But no matter how terraforming occurs, it will take a long time, lots of resources, and money. I doubt we'll live long enough to see people colonizing on Mars.
It's not a matter of time. There's only so much gas available and pumping it into a dissolving atmosphere isn't worth it. Some examples of helium running low, the gas that we just let go into the atmosphere for the amusement of a floating balloon that has some other uses, medical purposes.