How to mine asteroids...

When I'm running on the track, I imagine how the whole thing goes down. Candidate asteroids are discovered using space-based telescopes.

Phase 1. Once a suitable rock has been found Robotic swarms are sent to the asteroid to establish composition, etc. A Optoelectric nuclear battery propulsion is affixed to provide gradual thrust over time.

Phase 2. An atomic bomb is used in outer space to "nudge" the asteroid on a path towards an earth lagrangian point. A copper/zirconium disc may be used to impact with the asteroid, (similar, in principle, to those desk toys with the metal bearings suspended on strings that hit each other back and forth.)

Phase 3. Anchors for a solar sail are fixed onto the asteroid during phase 1, and a solar sail deployed. Sail compliments the opto-nuclear propulsion engine(s).

Phase 4. Asteroid transits to desired near-earth location.

Phase 5. As the rock closes in on it's destination, solar sail is decoupled using explosive bolts. Asteroid is flipped about it's axis and propulsion engine is used to provide braking. If necessary another atomic bomb may be used to de-accelerate the asteroid

Phase 6. Mining operations begin. Haven't figured that out yet. But let's bring a ~40-60km asteroid full of platinum, rhodium and who knows what else and pay off the national debt? X-Ray lasers are used to cut into rock, spallation is collected in appropriate medium (aerogel?) for return to earth and final processing.

Phase 7. Profit!