Soundproofing a home music studio doesn't necessarily require expensive materials or acoustical engineering expertise. If your goal is simply to deaden an annoying echo, or to placate an irritated neighbor, you can achieve a decent amount of soundproofing with salvaged carpeting and old couch cushions. In addition to hanging sound-absorbing materials on the walls, look for ways to deaden other hard surfaces, and remember to tend to windows and doors that may be leaking or letting in noise.
Find the "sensitive" spots of the room. These spots are easy to find — stand in the middle of the room and clap your hands loudly. Carefully note how sound bounces off the walls; go around the room clapping your hands until you pinpoint all of the spots that reflect the noise. You'll need to insulate all of them.
Hang a layer of carpet on the walls that need it, securing the carpet with small nails. Superglue may be necessary to hold the carpet flush against the wall. Note that some people will simply insulate a whole room if they want it completely "dead." However, padding down the whole room will also cause your vocals to sound "emotionless," meaning they have no natural reverb from the room.
Once you've put the carpet on the wall everywhere you want it, start placing the couch foam over the carpet layer. Secure the couch foam with small nails — you may need a nail gun to do this since the both the foam and the carpeting are thick. Try not to overlap the couch foam, as this will affect your overall vocal sound. The vocals will bounce off the uneven foam, which may cause them to sound slightly distorted.
Do another sound test. This time, stand in the center of the room and yell to detect any echo. Having a little echo is a good thing; however, if the room doesn't have enough padding you will hear the echo bounce off the walls, which is a bad thing. In the latter case, add more padding around those super-sensitive parts of the room.