Select a space. A basement room or room with no windows is ideal. Remove everything from the room, as the entire space will need to be insulated. Concrete walls are better than wood.
Mount soundproof foam blocks on all the walls and ceiling. The foam blocks can be glued or nailed into the structure. Soundproof foam ranges from a couple inches to several inches thick. Thicker means more insulation and less noise.
Attach soundproof panels to the walls and ceilings on top of the soundproof foam. The panels will finish the room quite nicely and also add another layer of soundproofing to the studio. The panels can be glued right on top of the foam blocks.
Use caulk to fill in the gaps between panels.
Lay out soundproof carpet on the ground. Soundproof carpeting comes with about an inch of soundproof insulation.
Cover any windows with soundproof foam and soundproof panels.