Instructables has published a short guide to building a music studio in an apartment:
You cannot build a sound studio without first understanding some theory. The most important part to understand is that sound proofing (blocking the sound, so others don’t hear you and you don’t hear them) is very different from sound treatment (making your room sound good). Since this studio was built for mixing sound and music for film and TV in a residential coop apartment building in NYC, both sound proofing and treatment had to be near perfect. It also had to look good for clients… on a very tight budget.
In this instructable rather than a tutorial on the actual construction I will discuss the design, with links to the materials I used or other resources.
The guide has a lot of info on sound proofing, sound treatment and also a little about using green materials, where possible.