There are four key points to reduce the level of sound going through a wall. The first main key to soundproofing is mass, according to Owens Corning every doubling of the weight of a wall the sound transmission loss will increase by 5-6 dB and being airtight. The second key is the wall must airtight, even a 10 ton wall won't help you if there is a hole in it, the sound will go right through it. If you are building a studio build it as heavy as you can and as airtight as submarine. The third and fourth points are more difficult to achieve on an existing wall they are breaking the vibration path and cavity absorption is to decouple the room from the rest of the building.
The first thing to do is plug any hole or gaps in the wall. A hole, gap or any air leak will lower the STC of the wall. The important thing to remember is the STC ratings are measured on perfect airtight wall so it is very easy for a wall with a rated STC of 30 to only have a STC of 20 in the real world. A small gap where the wall meets the floor is very common. That gap must be filled with chalk for the wall to meet the expectations.
In any room, the weak point for soundproofing will be the windows and doors. The STC of window or door with good seals will have rating of 20-28 dB. Without any seals, it will drop to about a STC 15. Most of the STC rating for windows found in acoustic books are for fixed windows (like you would see in a control room). A window that can be opened will have a lower STC rating than a fixed window, so existing windows to the outside (most of which can open) cause additional problems.
A poured concrete or brick wall will give you the best isolation (Transmission Loss). Walls are rated by what is called Sound Transmission Class (STC). The STC is an average dB loss of a wall for 125hz to 4000 Hz. A concrete wall may have a STC of 45 while Sheetrock and 2x4 wall may only have a STC of 30. The big problem is the concrete wall will cut 125hz bass frequencies by 30 dB but the gypsum board and 2x4 wall will only cut it 12 dB. Putting two layers of gypsum board on each side of the wall will increase it to 20dB. The heavier wall the better it can block the bass from going through it.