What's the best way to soundproof a room on budget

I'm starting to research ways to reduce sound transmission through a wall since I'll be moving in a few months and my new living space will share one wall with another family. What I am thinking is nailing cork board onto the wall and then covering the cork board with inexpensive foam pyramids. I think I could do thewholewall (8-9 feet high? 14 feet wide) for around $500-$600 dollars going this route. Any suggestions for whats worked for you?
Google Quietrock drywall. Excellent soundproofing and if your on a raised foundation make sure to insulate the subfloor. Good Luck.
MASS is the way to control (reduce) TRANSMISSION of sound
from one space to another (or from outside to inside.) Adding
stiffness to the dividing surface/partition can also help, but as
you will discover, it's pretty hard to add stiffness without adding
mass at the same time -- so back to 'square one' ;~)

FUZZ is the way to control sound WITHIN a space
(reverberation, decay, reflections, etc.)

There are refinements of course, including combining the two
(when 'tuning' your listening room, for instance) but those are
the TWO BASIC principals of SOUND CONTROL. These two
principles (and the differences between them) were drummed
into my head when I studied acoustics at MIT with Bob
Newman, a principal in the famous acoustical engineering firm
of Bolt, Beranek, and Newman.

So in your case, forget the 'fuzz' (the cork and foam) at least
insofar as addressing the sound transmission problem is
concerned (you may need it to 'tune' your listening room, but
that's not what you asked about.)

Budget? The least expensive (and least invasive) way to add
mass to (YOUR side of) the wall, assuming you've permission
from the landlord, is simply to add more drywall. Either
3/4" thick, or two layers of 1/2" thick drywall. For
ease of installation, you can use 4x8' sheets for an 8' ceiling, or
4x10' sheets for a 9' ceiling. There is one very effective cost-
and-labor-reducing trick however, if you can work out the
aesthetics ;~) which is to apply the additional drywall sheets
(one layer or two) as a 4' (high) band HORIZONTALLY and
halfway between the floor and ceiling, for the length of the wall.
This puts the additional mass where it will do the most good in
terms of keeping the wall from acting like a diaphragm and
transmitting the sound to the next space. The QuietRock
product that needfreestuff mentions is excellent for new
construction, where it will be the only wall material and may
have to meet new sound transmission codes; however for your
purposes (budget and retrofitting over existing drywall) it won't
be cost-effective, compared to 'ordinary' drywall ;~)

One other thing. Do make sure there are no actual LEAKS
between the two spaces -- any place air can go, sound can go.
This problem commonly occurs in cheap construction,
especially in the form of electrical outlets (boxes) have been
installed back-to-back for the two spaces! This also applies to
floors and ceilings where there are common attic and/or crawl
spaces. It doesn't seem like it would make that big a difference,
but it does! So take off all the wall plates and caulk your brains
If you add drywall also consider using Green Glue between the layers. It is not a glue, but rather a sound deadening compound. You can also use mass loaded vinyl.

This website has some good information on various methods and their effectiveness.

Sound Proofing Company

The biggest problem is deep bass. It is almost impossible to stop without major work.
I had Tony Manasian (of Tonian Labs) over at my apt. after I bought a pair of his speakers. His main gig is professional high end installations and consulting and he told me that bass is the hardest to control and advised me to hang some natural fibre mats or rugs behind my speaker to keep sound from transferring down to my neighbors below me.

It worked, to a point, depending on how loud I play my music. The bass is another problem since my speakers roll off around 40Hz. As for the courtyard and when I forget to close the windows, that is another matter.

Good luck,
If you can, stagger the studs in the wall so a stud is only connected to one panel of sheet rock. Then fill the wall with fiberglass insulation, snaking the insulation between the adjoining studs. That keeps the wall from becoming a drum, and damps out higher frequencies. We did this when building the house and it's amazing how well it works. Of course, your room will be two inches smaller :-)
Agreed - if you can do an isolated second wall that is a great solution. That option is discussed on the website I gave above. It is a great solution, although not always the easiest and less expensive.

You should also look at the resilient channel solutions, although they can be somewhat complicated to install.
C'mon guys (Dtc, Electroslacker); the man said he's on a budget. No way he's going to rip out and re-build his wall to install staggered studs for $500 - $600! And using resilient clips and/or channels to 'float' the drywall surface works best in new construction.

Trust me B_limo, adding another layer of sheetrock to the existing wall will get you 90% there without extra hassle/expense -- to say nothing of minimizing the 'noise inconvenience time' to your neighbors while you're doing the work ;~)
Nsgach - sorry, just providing ideas. If you do it your self, you can do these projects pretty cheaply. But I do agree that double walls and the like can be expensive if you have to pay someone to do it. In fact, I said that a double wall was not inexpensive. But also, this is not a very big wall.

My first recommendation was dry wall with green glue. Did you read the website I referenced? One level of drywall gives a STC of 40, adding a second level goes to 42, adding a second level with Green Glue goes to 52. Using Green Glue with drywall will do a lot more than just adding drywall. Green Glue is not cheap, but it really is effective. Mass is great, but isolating the surfaces is very efficient. Green Glue does a good job of that, by essentially turning the sound into heat, as I understand it. If you have not used it, you should look into it.

1 Layer of Drywall STC 40
2 Layers of Drywall STC 42
2 Layers of Drywall with Green Glue STC 52
I did check that site Dtc (denver tech center? Im in the springs).
I'm wondering how much green glue you need, and if it would work out, I guess I could ghrow some green glue on the backside of sheetrock and nail it up myself and then pay someone to come spray some texture on the wall and then paint it myself. That shouldn't cost too much.

Another option is to just put green glue in the homeowners ears...
They recommend 2 tubes per 4x8 sheet. Green Glue has their own website with recommendations and pricing. 12 tubes is about $150. It is not cheap, but works better than just using straight dry wall. I used in the ceiling of basement when I finished it for a theater. Really does cut down the sound transmission. There used to be a lot of discussion of sound proofing on AVSform in the Home Theater forum. Not sure how active it is these days, but still lots of good information. Ted White from my previous link used to be active there. That is how I got to his site.