Assess your situation and desired result, and make a detailed drawing of your space to plan out the installation of acoustic materials. Factors such as the type of noise or sound, amount of decibel-level reduction desired, room configuration and other environmental factors will determine the best acoustic material for you.
Install cardboard egg cartons or crates for an inexpensive DIY acoustic material that has been employed by garage bands and drummers for many years. Glue, staple or nail the egg cartons to the walls of your space. Although they will not completely dampen the sound, they will provide a low level of decibel reduction.
Staple or nail pieces of carpet and/or carpet padding onto the ceiling or affix to the wall to provide a slightly higher level of sound isolation. Thick-pile, "shag" rugs will provide better sound dampening than a low-pile carpet.
Attach foam padding, which provides a high level of sound isolation and can be found in various thicknesses. It can be stuffed into tight spaces or affixed to the walls of your space using staples or glue.
Utilize Styrofoam padding, which comes in various thicknesses and shapes, as well as in a variety of inexpensive products such as coolers or packing material. Styrofoam can be glued to walls or doors to provide a sound barrier or broken into pieces and placed inside drums or amps to deaden the sound.
Reuse old mattresses and pillows. Pillows can be placed inside drums to deaden the sound. Mattresses can be hung on the wall or placed in front of a drum set or amp to reduce the sound level.
Spare or scrap fiberglass home insulation can be installed with nails or staples onto your walls. Fiberglass insulation is available in rolls or hard panels, and it can be cut with a box knife.