Soundproofing an existing room in a house is an extremely difficult thing to do. All you can do is remove all the interior wall paneling and fill the space with acoustic foam batts. That's the easy part.
Then you have to replace the wall paneling with a double layer of Gyprock. Preferably of two different thicknesses. But before adding the second layer you have to apply "green glue" all over the back of the second layer panels. This applies a non-resonating and a sound absorbing film between the two layers, when the second layer is affixed to the first layer.
The next thing is the door to the room. If it's a standard core panel door, you will have to replace it with a solid timber door. Then you will need to seal the space between the door and the frame, using the acoustic foam / rubber stripping around the perimeter of the frame
Following that is the floor. Any existing floor covering will need to be removed, down to the floor boards or concrete and then completely covered with acoustic underlay. Then covered with a deep pile carpet. This will help with acoustics and sound transmission through the floor.
Last of all is the ceiling. Completely covering the ceiling with acoustic foam inside the ceiling will help, but won't make it completely soundproof. Covering the ceiling with "egg crate" foam on the underside will also help to reduce sound levels.
The end result will significantly reduce sound transmission but it will not be totally sound proof. - Prof
I've experimented with soundproofing using bubble wrap as a cheaper alternative to sound proof foam pads and also bought rubber matts for the floor. I also picked up timber pallets with a view to make them into portable sound proof panels on wheels. After seeing a pallet project here for a bar, I thought if it was feasible to take that idea further and make a recording booth too! - gc
I'd certainly be interested to see if you could incorporate Sounds Screen insulation into the interior of the pallets and then potentially add outer skins to them with plywood on either side. Any additional layer that you add to the walls would assist in inhibiting sound transfer.
It might be worth investigating whether you could find either egg crate mattress topper or sheets of egg carton at a budget price. They could be available for a cheaper price than proprietary sound insulation panels. - MitchellMc
I have recently been in discussion (and had a useful outcome) with a professional regarding sound lowering in my bedroom, but for the purpose of sleeping despite the noisy neighbours at night. The advice was that it is the density of the material that provides sound absorption, not the shape, nor necessarily the thickness.
Egg carton material, which has density, is more often used to absorb sounds and is better at it than normal low-density foam rubber, which is usually made to absorb some body weight for comfort. The egg-carton shape provides less reflection as well as more surface area to do so.
Bubble wrap may provide less sound reflection than hard walls (and will at least let in window light). Heavy curtains could do so more aesthetically, if that's any issue.
For my situation, we had double-glazed windows installed, mostly to lower heat transfer and some sound absorption, but I felt (correctly) that the neighbours' voices were arriving through the ceiling. After the advice, we had a layer of heavy density insulation which is designed to absorb sound (less so heat) put in the bedroom ceilings, topped with a layer of normal insulation for the heat. Result: now have barely noticeable sounds in the bedroom, which is exactly what we wanted... to be 100% sound-proof would have felt eerie in my situation. We can sleep peacefully. - TedBear
We did some research and realise our "hollow core" door is one of the things that we need to get rid of and also a large gap between door and floor. - ivanptr
To further increase your soundproofing I suggest using Raven 5m Superior White Door and Window Weather Strip - RP59 White. Place the weatherstrip on the inside channel of the door frame to cancel out the noise coming through the gaps. Here is a catalog on one of our door sets: Hume Doors - EricL