The trick to this method is that the drywall panels are hung on a pair (or more) of wooden "cleats" made from a sliced 2x4. The upper cleat on the back of the drywall is isolated from the lower cleat on the wall behind by inexpensive closed-cell foam tape. No part of the outer and inner walls touch directly. In practice, very little sound is transmitted through the foam, and the walls achieve a very high degree of soundproofing. The weight of the drywall keeps it in place so surprisingly well, that I use only two cleats: one near the top and one across the middle.
Overall, this method is fairly easy. It's not nearly as quick as using resilient channel, because it involves splitting a 2x4 lengthwise. (In either method, you will want to use foam tape to add extra soundproofing, so this extra step isn't a tradeoff, unless you choose to buy the resilient-channel pre-taped. The parts list is very small - drywall, a table saw or bandsaw, one 2x4 for every 4x8 drywall panel, nails, drywall screws, foam strips, and some pipe insulation. Surprisingly, this method requires much less precision than you would think, because some mistakes are in a sense self-correcting. Of course, the DIY version of this method does assume skill and confident use of limb-shearing power tools to do a potentially-dangerous "rip cut". If you don't have a woodworker's confidence with this step, find someone who can do it for you. A great recommended alternative is to have the lumberyard cut the wood for you upon purchase. In the section on ripping the wood, I'll tell you what to say to get the cut we want.
Since soundproofing carries with it a lot of myths and misconceptions, this Instructable will start with a little soundproofing theory before heading into the steps.