If you’re living in an upper-story apartment, you’ll most likely want to soundproof your floors. The most economical way to soundproof floors is to lay down a thick and heavy carpet. You don’t even need to install it -- just laying it down on top of the existing one will work sufficiently. The thicker the carpet, the more effectively the sound will be stopped.
If your landlord agrees, buy some caulk and seal off the sides of your windows and doors. There are special caulks -- known as “acoustical caulks" -- specifically designed to deaden sound. If you can spend a little more money, find this type; otherwise, traditional caulk will be sufficient. Apply the caulk in all cracks and gaps found around the doors and windows. If your windows have thin glass, adding heavy drapes can also help prevent excess noise.
There are two cheap options for walls: use acoustic texture or add another layer of material. Acoustic textures are special types of textured paints that help deaden sound. Find spray-on acoustic textures as they are the cheapest to purchase and easiest to apply. If you’re not allowed to refinish your walls, put up thick wall hangings and cover as much area of the wall as you can. You can do this by installing a few hooks at the top of your walls to hold thick and heavy cloth. You can also add wall designs; each wall design, whether a cheap painting or drapery, helps in stopping sound from traveling.
As with walls, ceilings need to be made thicker so the sound won’t travel through them. Applying acoustic texture can help, as can as covering the ceiling with acoustic mats. Like acoustic textures, acoustic mats are special materials designed to deaden sound. If you have access to the upper floor, lay down carpet on the upper floor as well.