The first thing to note is that sound treatment and sound proofing are not the same thing. Sound proofing is about making things sound quiet. Sound treatment is about making things sound good. These things really are mutually exclusive.
Consider the recordings you have made on your phone, or with a video camera of everyone singing Happy Birthday to grandma on her 90th birthday. You know that hollow, boxy sound? People blame it on cheap microphones. That may be partly true, but the bigger culprit is a lack of sound treatment in the room. What happens is that sound waves are hitting hard surfaces and reflecting off of them, and ultimately, back into the microphone. In a very large room, you’ll hear a natural reverberation or maybe even an echo. In a smaller room, those sounds will be so close together that they will just smear and make a mess. So, there are two factors at work here - the size and shape of the room, and the reflective surfaces.
Imagine a 10x10x10 room with a sound source exactly in the middle. The sound travels from the source and bounces off the walls and around the room. Because all of the surfaces are pretty much equidistant, the reflections make a huge mess in the center. That is, admittedly, over-simplified, but it gives you a sense of where some of the problems do lie. One remedy to this problem is to construct the room so that the length, width and height are not even multiples of each other.
Reflections can also be controlled by angling the walls. In a square room, the walls are parallel, and the corners are square. Sound bounces off them and off each other quite a lot, with bass frequencies taking up residence in the corners. Many recording and mixing spaces are constructed to be pentagonal and with a sloped ceiling - no parallel surfaces to reflect sounds back into the middle of the room, and no square corners for them to build up in.
But the size and shape of the room are usually already predetermined. Your final solution is to add material to the walls (and the ceiling and floor!) to absorb some of those reflections. Be careful, though, as you don’t want to over-do it. A typical material is semi-rigid fiberglass, such as Owens-Corning 703 is the go-to product. This can be difficult to find in Canada but was able to locate a very similar material in Stoney Creek at Glass-Cell Iso Fab. They have other locations in Ontario. http://www.glasscellisofab.com/en/contact.html As a last resort, you could source out some Roxul “Safe and Sound,” but it is NOT the same thing.
Here is a sequence of photos that shows how I built my own absorptive panels, including a “cloud” for my home studio.
The link also shows how I built what are called “bass traps” in the corners. Bass traps help to prevent sounds from building up in the corners of rooms. Low frequencies are particularly subject to this, which really does mess with how sound is perceived and distributed in the room. Essentially, a bass trap is a triangular wedge that absorbs frequencies, while minimizing the “squareness” of the corner.
The difference this makes is truly remarkable. Before treating my room, I did a frequency response measurement of my space, and it was horrifying. I had some frequencies that were represented literally more than twice as loud or twice as quiet as others that were only a few notes away. No wonder I couldn’t mix anything to save my life! Now, with some changes made to how and where I was placing my monitors, along with my acoustic panels, the room is flat from about 60hz to almost 20khz, within +/- 3db. It’s not perfect, but I can mix in there now with confidence that what I am hearing in my room when I mix will successfully translate to other systems in other rooms.
There is no such thing as cheap soundproofing. It's complicated, and it's expensive. Anything that does not match that description is going to be dodgy at best.
Essentially, soundproofing comes down to a simple formula:
mass + insulation (even air space is fine) + mass = soundproof. The effectiveness of this equation is dependent upon how much mass you have, the quality of insulation, and how air-tight the air space is.
Generally, what is done to soundproof a space is to build a room within the room such that the floor, walls and ceilings are not connected to the outer floor, walls or ceiling with anything that will transfer vibration.
The "outer room" will have studs placed not against the wall, but in from the wall a little bit. The wall frames and floor of the "inner room" will be elevated and placed on dense absorptive foam rubber or similar material. The "inner room" will also be connected to the ceiling of the outer room with a similar kind of material. The "inner room" will be constructed with drywall or something - maybe double-thickness - placed on *both* sides of the studs. This gives you an airspace between the two layers of drywall, and an air space between that and the outer room.
The studs for the walls will also typically be offset from one another so that the outer wall and the inner wall do not touch - almost like one frame for the outer part of the wall and another frame for the inner part of the wall.
Think of this... you know that old trick with the tin cans and the string where the sound travels along the string? Well, you can sound-proof the crap out of your walls and ceiling, but the sound will travel along the floor across the joists and follow the joists to the outside. Similarly, if your inner room and outer room are connected... say... the screws for the drywall going into the studs, and then those same studs touching the outer layer of drywall, you have the potential for sound transference from the inside to the outside.
Think of this too.... sound travels through the air in waves. That means that if air can get out, then logic says that sound can get out. No prob.... just block off all the air holes with enough mass and insulation and enough mass again to absorb all the sound waves. Er... wait a sec..... but if air can't get out.... how can it get in? Ooops.
Oh, the egg cartons.... the reason they don't work.... practically no mass! And they typically get installed such that they touch the walls, so sound travels through them to the wall and to the outside.
I STRONGLY advise three resources:
This book is written in very friendly language, and is really well explained. I can't recommend it enough. I have it. The author is Rod Gervais, and the book is, by most people's standards, the bible on building a home (or garage) studio. It also recommends techniques, materials, a bit of acoustical physics, etc.
This forum is hands-down the best resource on the internet for studio construction. John Sayers builds studios into the 100's of thousands of dollars and you can see his work on the site. He frequents the forum. Rod Gervais, the author of the book above also frequents the forum. So do many other bedroom experts, as well as many who are actually acoustical engineers.
Ethan Winer is the developer of a company called Real Traps, an industry leader that specializes in acoustic room treatments. This is his acoustics forum, and he posts there frequently.