Acoustic insulation on its own cannot fully reduce all noises by itself.  The wall framing style and materials in the space will determine just how hard the existing room will be to achieve good soundproofing.  Building a new room that requires sound proof insulation allows for off setting the studs.  The off-set stud wall style stops vibrations sound waves from being transferred directly by hard dense materials like wood or metal studs that connect directly to gypsum board, also called sheetrock, on each side.

Acoustic sound insulation creates space where the sound vibration has trouble crossing.  The wider the space the harder it is for sound to cross.  Less dense materials also cause disruption of sound transfer.  Hit a wood table with a hammer, you get a loud sound.  Hit a mattress on a bed, you get little sound.  A wall with offset studs and a continuous layer of uninterrupted sound proof layers on the inside is good a great noise reduction design.

Ceilings can cause special problems when retrofitting a room.  Ceilings may not have windows, but many mechanical systems come through them like air conditioning ducts and outlets.  If your room is required to be extremely quiet these systems will have to be either shut down or isolated.  You never know how noisy a rattle in a light fixture can be until it rattles in your sound proof room.  Various sponge tape and pressurized cans of foam can help dampen these little nuisance noises like light fixtures, wall plugs, and wall switches.  If you use spray foam space fillers, it is extremely important to check the fire resistive capabilities before applying it to electrical devices.

Acoustical insulation applied to the surface of existing walls and ceilings will certainly help make your quieter.  Doors and windows cause another special problem because the goal in sound proofing is to achieve a continuous uninterrupted barrier to block the sound.  If you can cover the doors and the windows either permanently or temporarily, you will achieve a quieter space.