I’ve always found asteroids to be fascinating. They are often surprisingly big, they contain a wealth of information about the history of the Solar System… and, let’s be honest, they’re frightening.
There are thousands of asteroids out there, often collecting in clearly defined belts or gravitationally stable regions known as Lagrangian points. However, many are not so well behaved; they seem to have their own agenda, flying around the Solar System in their own orbits, sometimes buzzing the Earth.
Fortunately, the vast majority of these rocks are harmless; if they hit our atmosphere they might create a dazzling light show, burning up, possibly even exploding as a fireball. Sometimes though, a big asteroid might be observed and astronomers become a little concerned. The next known threat that might hit us is the famous asteroid named Apophis that is expected to make an uncomfortably close encounter with Earth on April 13th, 2036. The odds of Apophis hitting us in 2036 (not 2029 as quoted in the above video) are 45,000:1, which may sound fairly unlikely, but if you start comparing those odds with dying in a plane crash, or being hit by a car, you’ll see that actually, a one in 45,000 chance are the kind of odds you’d happily quote when placing a bet in a Vegas casino. I have a chance!
Yes, and there’s also a chance of a 350 metre-wide asteroid hitting us in 2036, so perhaps we should start planning for the worst?
Fortunately, we have some lead time on Apophis, and we’ll learn more about the chunk of rock when it flies past the Earth in 2029. And that’s what it’s all about: lead time. If mankind spots a potentially deadly asteroid approaching us, we’ll need as much time as possible to nudge it off course.
In a video I just stumbled across on Discovery.com, Joseph A. Nuth III from NASA Goddard Spaceflight Center shares his views on what we could do to prevent a potential asteroid catastrophe. By developing asteroid deflection techniques, we’ll also be presented with an opportunity. As pointed out by Nuth, if we have the ability to deflect an asteroid, perhaps we can steer it into lunar orbit, so we can carry out mining operations…
astroengine.com 
The most difficult thing about steering an asteroid into a nearby orbit (high-Earth or lunar orbit) is that once you get it into our gravity well, you have to slow it down to prevent it from leaving again. Since asteroids tend to lack an effective means of propulsion, there are two potential ways of accomplishing this. One would be an anti-slingshot maneuver (opposite of what we sometimes do with our deep space probes), and the other would be to let the big rock skim the upper atmosphere.
Obviously, there is going to be some opposition to the latter approach unless you can demonstrate that you have very precise control over the trajectory of the rock. Even then, I doubt you’d be allowed to try it with any thing large enough to cause any trouble if it were to fall completely to Earth.
The first proposal, however, could possibly work. There is still a chance that you could inadvertently divert the asteroid towards the Earth rather than into a nice parking orbit, but steps could be taken to minimize that outcome. The precise orbital mechanics would probably be a nightmare to work out, and would most likely need to involve multiple passes. We’ll leave the details as an exercise for the reader.
If what you want is a significant amount of raw material in a Luna-proximate orbit, you could always slam a fair size asteroid into the far side of the moon at a high angle of incidence. Depending on the size of the impactor, the glancing blow would likely throw up tons of material into cis-lunar space. Of course, all of the resultant debris would probably become a hazard to navigation, making it retrieval of the material almost impossible.
Long story short.. if you want to mine asteroids, you should probably go to them rather than try bringing them to you.