I'm not sure which video of Scott's you're referring to, but I doubt he cheated, although he may have used mods.
The easiest asteroids to intercept are the ones that enter Kerbin's sphere of influence, for obvious reasons. They're, of course, also the easiest to get captured. There are two ideas as to how you should go about getting the intercept: you can launch into an orbit that roughly follows the target asteroid, much like a standard intercept, albeit at a much higher altitude, or you can launch into an orbit that goes in the opposite direction of the target asteroid so that you can close the distance very quickly. They each have their advantages, but both require gobs and gobs of delta-V. Seriously, you're going to need a big rocket for this. I wouldn't worry too much about efficiency on this mission, since it's likely to just go down the drain with the numerous course corrections you'll be doing anyway.
In both cases, you'll want to wait until the orbital plane of the asteroid crosses your launch site, just like a normal intercept. Of course you don't absolutely have to do this, but it does greatly simplify things. You'll also want the asteroid to just be entering Kerbin's sphere of influence, since you otherwise won't have enough time to catch it.
So in the first case where you're going to orbit in the same direction as the asteriod, you can choose to launch when the launch site is on the same side as the asteroid, or the opposite side. Your rocket design, along with what mods you're running (particularly Farram Aerospace Research) may dictate that you choose the near side launch, since it doesn't require a gravity turn, which is generally already difficult with large rockets.
So launching from the near side, you'll basically want to use the entire first stage to go straight up. This should get your apoapsis height up to several thousand kilometers. You may need to use your second stage here as well. You don't want to have your orbit extend beyond the orbit of the target asteroid, as it's likely to just pass you by. Instead, put a maneuver node down at the apoapsis, and add prograde velocity until the planned orbit crosses the orbit of the asteroid. If it's showing a good close approach, congratulations, your hard work is already done, and it's basically just down to a standard rendezvous. If the planned intercept shows that you'll be significantly ahead of the asteroid, add some more prograde speed right now in order to delay your apoapsis. If you're going to be behind the asteroid, that's fine too, you'll just have to burn in the negative-radial direction before you reach apoapsis.
Once you've completed your apoapsis burn, you should have a closest approach within a couple hundred kilometers. It actually doesn't need to be any closer than that at this point. Switch the nav ball to target mode, and check that your relative velocity is in approximately the same direction as the target indicator; within 15° should be sufficient. Closing speed doesn't really matter here, since it might be as low as a few hundred meters per second up to a few thousand meters per second. Time warp for a bit, correct your relative velocity, keeping the closing speed fairly high until you're "close" or get a good intercept, rinse and repeat. It's these corrections that consume so much fuel, and while it's not very efficient, it's much more fool-proof than playing with maneuver nodes. Once you're close, it's just a standard rendezvous.
If you think your rocket can make a gravity turn, you can try the second option for orbiting the same direction. You can launch from either the near side or far side of Kerbin, and if you're really lucky and your target asteroid is near the equatorial plane, at just about any time. You'll want to launch into a low orbit, and once situated, create a maneuver node that will intersect with the orbit of the target asteroid. You usually want this intersect to be before the periapsis of the asteroid. If the closest approach indicator shows that the asteroid is going to be significantly beyond the intercept point, well tough luck, you're going to miss this one. If it's going to be significantly behind, you can delay your burn by one or more orbits to bring it closer. If it's only a little ahead or behind (even after delaying your burn by some orbits), you can play around with the location of the maneuver node to get it closer. If that still doesn't do the trick, don't fret — you'll just have to spend some extra delta-V using the previous procedure.
For the daring, there's the third option. Basically, your goal is to closely match the path that the target asteroid is taking, but go in the opposite direction. You don't have to exactly match the orbit — having an orbit that leaves Kerbin's sphere of influence isn't even necessary — but your orbit needs to be relatively close to the asteroid's orbit for a fairly long stretch. I suspect that this is the method Scott Manley was using in the video you mentioned. When doing this type of encounter, I find launching from the far side of Kerbin is easiest since it's closer to the periapsis of the asteroid. It's at the asteroid periapsis that you want to make your intercept burn, turning your orbit into one that's highly elliptical, if not hyperbolic. This is daring because your closing speed will be twice your orbital speed — easily several kilometers per second — and you have to kill that relative speed quite quickly. This is all before you even capture the asteroid as well. I should also note that this procedure works best when the asteroid has a relatively low Kerbin periapsis.
None of the procedures are terribly easy, but they don't have to be very hard either. Experiment while you're performing them by making various off axis burns to see if that improves your situation, or makes it worse; it'll help you in the long run by hopefully improving your orbital intuition, which is not an intuitive subject to begin with.