I find it freaking awesome that we've progressed to the point that we can discuss means of terraforming another planet that are actually within our current technological grasp (if not necessarily financial). As another pointed out though, how do we go about generally a large enough magnetic field to prevent the newly liberated atmosphere (from the polar ice) from bleeding off into space?
Warm the place up - Check.
Increase atmospheric pressure - Check.
Keep the place from going tits up, again - ??
Btw, the required materials already exist, but sorry, phobos and Deimos, one of you has to die.
It would take at a minimum hundreds of thousands of years to ablate the atmosphere with solar winds...dropping a comet or two in (using an atmospheric perigee, but extremely elliptical orbit to ensure minimal chance of surface impact, in a argument of perigee stable orbit (to ensure eventual impact is polar) should suffice.
The biggest issue with no magnetosphere is lack of shielding, so it's underground living, sorry.
Artificially creating a magnetosphere is hard. You could do it by stringing a superconducting cable all the way around the planet (in orbit) and charging it up, but it would take cubic kilometers of materials to make. It would be a near permanent solution though, not to mention a good platform for a low altitude synchronous platform by using it as a dynamic compression member.