There many ways to make this happen. It depends on your available equipment and budget.
I'll represent one of the possible ways.
1.Adjust tick wall frames toward the wall. (it could be anything like library bookcases)
2.Adjust dry walls onto them.
3.Most walls usually have one row of studs, you can create two row of studs and place one beside each interior but keep some of the gabs in order to be able to add more dry walls later on or other adjustments.
4.Use resilient channel and screw them into the studs to help to cover the reflections and the sounds.
5.Adjust damping compound you can also get along with fiberglass.
6.The next thing you need is Acoustical caulk to fill the left out gabs and cracks.
7.Use soundproof floor and ceilings.
8.Install soundproofing panels.
9.Done
For each tool you can do a little research from those who are in this business and also use internet to get more detailed information. Because it's a bit hard to explain such a thing very widely and detailed in here. But i gave you an idea, so you could follow it up and get more information off of it. Hope it helps.
Good Luck.