First, the criteria. Makes Mar’s habitable. Not by having people living in contained bubbles, but by making Mars have a breathable atmosphere, livable average tempuratures, and be able to support agriculture and wildlife. What would it take? What would be the best way to go about it? How long from now? 10 years? 50? 100? 500?
I believe that one of the biggest problems is that mars has insufficient gravity to maintain a breathable atmosphere without constantly topping it up.
My wife tells me I am very habitual. Or habitable. Or something like that.
I think the current scientific consensus is that since Mars doesn’t have a magnetic field anymore any substantial atmosphere would just be blown away by the solar wind. So it’s bubbles or nothing for us if we want to live there, at least until we find a way to generate a constant planetary magnetic field - which is slightly beyond existing technological capabilities. 
I do recall a early 20th century writer who suggested we crash a big rocket full of Aerasol sprays on Mars. Which would then form an atmosohere.
Carl Sagan, in Cosmos, proposed that we seed Mars with dark-colored plants. This would increase the amount of surface heating Mars receives (by reducing its albedo) and at the same time turn all that CO[sub]2[/sub] in the Martian atmosphere into oxygen via photosynthesis. Plus, the plants will multiply and spread across the planet on their own.
Obvious problems with this scenario:[ol][li]The Martian soil is about as hospitable to terrestrial plant life as bleach,[/li][li]Although the Martian atmosphere is indeed composed almost entirely of CO[sub]2[/sub], it’s at something like 0.005 atmospheres pressure, which isn’t much thicker than a vacuum,[/li][li]The plants would have to be able to dig really deep below the Martian surface to find sufficient water to live, and[/li]When they do hit water, it’s gonna be frozen, 'cause Mars is coooooooold.[/ol]
I remember reading about crashing comets from the Oort cloud into Mars. It’ll put a lot of dust in the atmosphere generating a greenhouse effect as well as adding water and gases.
I have no idea if it’s work.
fwiw There is a series of Books by Kim Stanley Robinson (RED MARS, GREEN MARS, BLUE MARS) that outlines a plan to do this.
Besides the stuff mentioned I’d add (to) the point that there is really no air pressure on Mars. Even if its thin wispy atmosphere was an appropriate Nitrogen Oxygen mix, our heads would still explode like Arnie’s enemies at the end of Total Recall…
A possible back of the envelope terraforming plan: giant mirrors reflecting sunlight to the surface to raise the temperature, melting what we know is in the Southern cap & subsoil. If you could ever get the temperature to rise to 70 degrees Celsius liquid water and weather appear, water would raise the atmospheric pressure to the equivalent of some earth mountaintops (except for Mar’s mountaintops).
Then add some super designer biotech bugs that eat the Martian soil and excrete nitrogen or oxygen. I think that they could work fast.
Total time would take decades at least. But hey, when it was over, holy crap we’d have a new planet next-door
You could increase the mass, and therefore the gravity, by slamming in a few extra moons and asteroids…
It’d take quite a few to make a difference, though, I’d bet.
Then there’s the problem of not having a magnetic field, meaning all the animals and plants are getting bombarded with radiation.
Why are humans so rabid about creating other habitable planets when we are trying so hard to make this planet inhabitable?
koawala: precisely because they fear running out of original planet, but are not about to stop doing their thing, either.
As to the OP, jimmy and others have pointed to the possible scenarios for terraforming Mars, which involves many of the difficulties tracer and others mentioned. Any scenario involves heavy planetary engineering. External climate modification by crashing asteroids, or using reflectors requires developing the capacity to perform those tasks reliably, consistently and safely across the Solar System. Not likely in less than 50 years, absent a 1960s-like “space race” (not so much because we lack the theoretical knowledge, technical skill, or industrial capacity to build the hardware and software for it, as for the literally astronomical cost) . Biological seeding would start first with bacteria resistant to current conditions – that’s some major genetic engineering right there, but it could be doable in that time frame.
In any case, even once the project could be started, we may not want to start it right away but wait until we have studied the planed in-depth BEFORE mucking around with it. So pop in another couple of centuries.
Then once we do start, we may be talking multiple millennia. First, the gengineering of the bacteria would perforce need to also speed up their action. Under purely natural conditions it took the cyanobacteria and algae, what, a billion years? to replace Earth’s original atmosphere with something passingly resembling an oxydizing mix. I don’t think we’s be that patient. A really fast scenario would IMO require a whopping leap in microgenetic or, more likely, nanotechnological engineering, so after cometary bombardment and/or release of liquid water/trapped gases, you could swarm the place with “designer bugs” (biological or nanomechanical) that would dismantle and reassemble the environment in a furious hurry, then either self-destruct or mutate into harmlesness, so you can drop in the next layer, lather, rinse, repeat, until you get an inhabitable environment. And all that has to happen without the whole thing or any of its parts evolving into something that would “reject” further transplants from Earth!