Hello Joe. There has been enough info posted on this subject to fill several volumes. But I'll try to break it down in simple terms.
There are two areas of construction that must be addressed for a studio or vocal booth/room acoustics.
Sound transmission and acoustical treatment.
They both have to do with the Physics of sound. Which in a nutshell is still not TOTALLY understood, even by professionals. But enough of it is well documented to formulate simple strategies for dealing with normal day to day home environments.
The FIRST thing you need to understand is DB Profile. Why build a system of assemblies that will attenuate 90db of sound when you only need to attenuate 45db. In laymans terms, why build something to keep the sound of a stack of marshall amps from entering a neighbors bedroom, when you are only recording an acoustic guitar? Does that make sense? It does when you consider that it takes TEN times the attenuation ability of an assembly to attenuate EACH additional db. That translates into money/time. This is the first thing you must evaluate. The type of sounds that will be produced will determine not only the type of assemblies, but materials as well. The second thing is determining your existing noise floor-i.e.....adjacent airports, trucking, foundaries, traintracks....you know.....sound that penetrates into your space. That translates into your tolerance for intrusion into your recordings. Third, who and what you are trying to keep your sound from bothering, and where they are located in relationship to you..i.e......a neighbors bedroom right above your studio.....not good.

Forth..existing construction....i.e. how and what your existing space is constructed of. A typical stick built bedroom will require a different set of materials, than an existing concrete basement. Understand?
From those determinations, a set of assembly criteria can be formulated. Only then will you be able to generate a materials list. Generally speaking, you can approach this from a budget viewpoint of total containment from the outset, or modify it to budgetary restraints. Bottom line though....sound attenuation is NOT CHEAP. Especially if you have train tracks within 50 ft of your house.

So, theres no sense in listing materials or types of assemblies untill YOU determine these things. There is NO one typical assembly for this stuff. Every project has its own set of criteria. Budget usually defines the level of attenuation, as it can be VERY EXPENSIVE to build a complete set of studio/control room/ iso room to attenuate lo frequency sound from adjacent neighbors, depending on all the circumstances listed above.
fitZ
