Comment use its own rotational kinetic energy! (Score 2, Interesting) 391
(1) Rendezvous with the asteroid. Time is important, so this will probably require a nuclear rocket.
(2) Construct a really strong anchor point, probably using a net around the entire asteriod.
(3) Construct a space elevator connected to the anchor. The asteriod will have much weaker gravity and much higher rotational velocity than the earth, so an elevator there wouldn't have to be nearly as long or strong as here. The motion of the asteriod may not be simple (precession in addition to rotation), which means the elevator will pivot about the anchor point.
(4) Use the elevator to launch payloads (bags of rubble). This doesn't require any net energy: a payload beyond the stationary orbit radius will pull outward, and can be used to lift the next payload. Each launch gives the asteroid a nudge (by conservation of momentum). You can't choose the direction of the nudges arbitrarily - assuming simple rotation, they have to be in the plane of rotation. Approximately twice a year, payloads can be launched toward earth. That would be a good time to send construction workers back home.