Doors and Windows
Cracks around doors and windows give sound a chance to escape into other rooms. To prevent this, the University of California, Santa Cruz, recommends sealing doors and windows with gaskets.
Rubber gaskets are flexible fillers for doors with sizable gaps between the edge of the door and the frame, while rubber and metal gaskets fill small cracks in doors that already fit snugly. If you have gaps between a door frame and a wall, fill them with spray polystyrene foam or caulk.
Seal windows with gaskets, too.
If you're worried about footsteps, carpet the room. Many apartment buildings have carpeted apartments and require tenants to keep the carpet, as this prevents footsteps from making sound, according to "UHF Magazine" Plush rugs are a budget-friendly alternative.
Although carpet cannot completely stop the transmission of sound, it absorbs much of it. Carpet is especially useful if your room is on an upper floor.
To prevent sound, especially low-frequency noises, from reverberating, place foam baffles against the walls. The foam absorbs much of the reverberation to prevent it from transmitting to the next room.
Cover vents in foam, too. Alternatively, panel the room in soft fiber board, followed by another layer of gypsum board.
Whatever method you choose, cover every wall in the room from floor to ceiling and, if possible, cover the ceiling. Paneling only one wall or only part of the walls will allow sound to escape as it did before, so make sure you can't see any of the original wall when you're done soundproofing.