In most cases, simply throwing some studio foam on the walls (although helpful) will not be sufficient. Properly sound-proofing a room is a very complex process that is best incorporated into the room during construction. It is possible, however, to achieve good results on an existing room by using correct techniques and materials.

Since sound-proofing a studio is such a complex and technical (and often expensive) undertaking, I recommend consulting with a professional to help you plan a strategy that fits your needs and budget.

Auralex has created a fantastic online resource about studio construction and acoustical treatments, Acoustics 101, which contains a wealth of information to get you started. You may also want to see our page on room acoustics.