How to actually mine Platinum Group Metals (PGM) from an asteroid, or my guess at how Planetary Resources might do it:
1) Find a metal-rich rubble pile (if they exist) with a PGM ore concentration of 100ppm (asteroids of that concentration of PGMs supposedly exist).
2) Pick off big metal chunks magnetically or somesuch.
3) After you have a thousand or so tons of metallic ore, put it in the shade to cool off to deep cryogenic temperatures.
4) Then, crush it in a grinder. Cooling the ore to cryogenic temperatures first should significantly reduce the energy needed to grind the ore to a fine powder, but grinding of ore often takes roughly ~10kWh/ton, so it'd take ~10MWh to grind the batch (or about 2 weeks if you have 30kW), although iron-nickel is pretty tough, which is why I included first cryogenically cooling the ore.
5) Grinding may heat up the ore, so it may take several steps where you grind, then cool, then grind.
6) Once the powder is fine enough, you put it in a vibratory centrifuge to clear off the relatively lightweight rocky bits (the metal will be much denser).
7) Then use a magnet to remove the powdered iron and nickle bits.
8) What you have left will be a MUCH more concentrated ore and a lot less material.
9) You can ship this back to Earth (a couple of tons to a few hundred kilograms... small enough to be returned to Earth, perhaps guided by a very small tug and perhaps with a very inexpensive heatshield) for sale or further processing.
10) Or do some wet-processing of the ore to concentrate it to PGMs (like dissolving the ore in acid... PGMs won't dissolve in most acids while everything else will, so you'll be left with fairly pure PGMs) before shipping back to Earth for sale.
However, acid processing may be too chemically intensive, and you might get by with just dry processing of the ore (although it sounds like Planetary Resources intends to do some wet processing, part of their motivation for focusing initially on extracting water).
At the end of this, you'll have about 100kg of PGMs, with a market price of roughly $15-30 million.
Rinse and repeat.
