Cut your wood planks to size for your wall. The 2 x 4-inch planks will be cut to the height of your room. The 2 x 6-inch planks will be used as the top and bottom plates of your wall. Cut the 2 x 6 planks to a size that will create workable frame sections. The more sections and separation, the more soundproof the finished wall will be.
Build your frame by nailing the 2 x 4 planks along a 2 x 6 base board in a staggered pattern. The pattern should alternate left and right, with the first 2 x 4 being nailed flush with the left edge, the second 2 x 4 being nailed flush with the right edge, and so on. Because both sides of drywall are hung on separate studs, there will be no direct path for the sound to travel through the wall, effectively soundproofing the structure. Finish the frame off with a 2 x 6 top plate.
Snake insulation in large pieces around the studs rather than cutting the insulation to fit in each section of the wall's frame. Because the framing boards are thinner than the base board, there should be ample space to work the insulation through the frame. The insulation will further isolate the boards from sound and vibration.
Hang drywall on the first side of the wall with screws. Attach the drywall only to boards flush with the side of the frame being covered. Use as few screws as possible to hold the drywall in place and do not attach the drywall tightly to the frame. Use construction adhesive to strengthen the bond of the drywall to the frame without providing excess sound pathways through screws. Making sure the wall is not fit too snug will allow for a buffer to cut back on vibrations. Repeat this process for the other side of the wall.
Use caulk to fill any gaps between the drywall and frame. The caulk will not only seal the wall, but will also provide a cushion to absorb sound waves.