People often mistakenly equate acoustic isolation and acoustic treatment. While both are integral to successful studio design, they have different goals. Acoustic treatment is the art and science of treating the interior surfaces of the studio and control room to achieve a desired balance between absorption of sound and controlled reflection. The usual goal is a certain "liveliness" that eliminates outright reflections and moderates the bass so it is even throughout the space, with no hot or dead spots.
Proper isolation eliminates unwanted outside sound from reaching your microphones. To a lesser extent, it is also about keeping the sound generated from within from leaking out and disturbing neighbors. The goal is to isolate the control room and studio space sufficiently so that sound vibrations cannot travel in or out through either the air or through the solid materials used for construction.
Acoustic isolation is achieved through decoupling and absorption. You will usually use a combination of both. Decoupling involves construction techniques that physically separate components such as interior walls, ceilings and floors from the rest of the building so that vibrations cannot travel in or out. Early radio studios that held large orchestras went so far as to hang the studio room itself on heavy cables from the surrounding building structure. These studios "floated," and sound vibrations were absorbed by the cables themselves.
There are many devices available from commercial vendors that can be used during construction to aid in decoupling. They usually incorporate components such as rubber cushions and springs to soak up the vibrations so that they do not further propagate sound.
When on a limited budget, you can still achieve good results by framing the studio and control room inside the outer room, resting the wall frames on rubber cushions to help decouple from the floor, and making sure the inner walls do not touch the outer walls, to decouple from the rest of the building. Wallboard ceilings can be mounted on frames that are hung with cables from the joists above to decouple from floors above (or the roof).
Absorption often depends on raw rigidity. Major studios often use two layers of 1-inch wallboard on the interior walls. Thick wallboard, concrete board (such as for bathrooms) and cinder block all absorb sound energy by virtue of their sheer denseness. They are also relatively inexpensive. Noise barriers and sound control products are available that are specifically designed to absorb sound through their material structure. They are targeted for particular applications or stubborn problems, and are sold in sheets, rolls or panels.
Surface-mounted treatment materials on the interior of the studio and control room will also help absorb sound from reaching the outside. However, they will do little to prevent outside sound from coming in.
Good isolation requires careful planning, but satisfactory results can be achieved even if you are on a limited budget.