NASA has actually published a study on this. This study was the primary motivator for Planetary Resources to start its work on mining an asteroid. And there is more work being done by NASA to learn more as well. And there's the approach that Planetary Resources has set in place, which seems to be the best overall approach.
The first thing that should be noted is that Asteroids have large amounts of precious metals. Estimates show that even a small asteroid could have a fortune in Platinum, at least at today's prices. Work would need to be done to ensure that the value didn't plummet the economy. But, there are other options as well out there as to how an asteroid could be valuable.
There are 3 primary types of asteroids. C-type, S-type, and M-type. The latter two contain significant amounts of iron, and the C type carbon. Now, metal on the ground is quite cheap. The cost of Iron Ore is about \$115 per ton. It would therefor be difficult to make money on Earth using Iron Ore. However, there is an alternative way to make money. The Falcon 9 has a cost per pound of \$1800+ if loaded to it's maximum capacity. Thus, if you can make something useful in space of your asteroid, it's value has suddenly increased dramatically. The key for the short term profitability in space is the ability to manufacture and otherwise assist satellites. The amount of money that can be made increases dramatically if you can pull it off. Rocket Fuel, which could easily be made from an asteroid, has the same cost of \$1800/pound, if you can get it to the source. It might even be worth more, as fuel would extend the lifetime of the satellites, which are significant investments.
So, what does it take to make a space mining operation profitable? Manufacturing. If you can develop an autonomous set of manufacturing robots, then you might be able to make something work. There is a number often quoted of \$2.6 billion to break even, but that depends on making these advanced robotics work. It could work, but I think only time will tell.
There is also a whole world of microgravity manufacturing possibilities which has barely been touched. It's far easier to make some things in microgravity, but we haven't really explored that space very much yet.
The closest we've done to real space mining is the Apollo program. In total, it brought 382 kg of rocks, for a cost of around \$125 billion in today's dollars. Asteroids would be cheaper to go to than the Moon, and using unmanned spacecraft should make it cheaper, but the proven numbers we have gives a cost of about \$9200/ounce (\$325/g). If that cost can be reduced, which should happen by making it unmanned and the primary mission, then gold could be profitable fairly soon.
The bottom line is, it's a long time before the Earth mining industry will be affected by Space Mining, but it would likely significantly affect the aerospace industry, moving operations to on orbit. And some day, some of those materials will return to Earth.