DahnBoson said:
The only way I can think of to get up that high enough times to mine it without burning a ridiculous amount of fuel is a space elevator, but that is a ways of itself.
Unless it is brought into an Earth (or moon) orbit somehow, the key point would be to send as few material as possible to the asteroid, and try to build something in place.
While there are some ideas how to
launch stuff cheaper than now, taking the material back to the surface is another issue, too. As far as I know, a space elevator and maybe tethers are the only structures which can do this without requiring a spacecraft every time. Of course, if launching costs are low, you can use a lot of heat-resistant shields for descent.
As far as I can see, we now have several different concepts here:
1) leave it in its orbit, use robots
2) leave it in its orbit, use humans
3) use robots to bring it into Earth orbit, use robots to mine it
4) use robots to bring it into Earth orbit, use humans to mine it
5) use humans to bring it into Earth orbit and mine it there
2 looks quite impractical in the next decades, and 5 would require expensive and long manned missions, too. 4 might be an interesting concept, if robotic mining is too tricky, but a simple mass driver can be installed without humans.