Obviously, you can't just send a bunch of out-of-work Kentucky coal miners up there to give it a go. You need some sort of specialized equipment. What I want to know is: what equipment will it be?
What machine(s) buildable with current day technology would allow you to economically mine a near-Earth asteroid?
Current day technology only
Must be launched into orbit by a rocket no more powerful than Saturn V (49 tons to a Lunar orbit). Multiple launches are fine.
For the elemental composition of the meteorite in question, use Table 2 here.
Must be able to remove useful ore and pack it in some way for transit. Returning the mined stuff to Earth is out of the scope of this question.
The key factor that must be considered is how much refining is to be done in space to make this economical. The edge case solution is just to return the whole asteroid to Earth and mine it on the surface after it cools down, but that seems a little too bombardment-y to be politically feasible.