You can probably do a search on these items as I am doing from memory from my construction days.

The interior walls.

 Build a double 2x4 wall for each wall. Keep a 1/2 " space between the walls at the bottom plate and top plates. Stagger the studs from the opposite wall.

Install sound batts in both walls. staggering the studs will eliminate voids for sound tansfer from other wall.

Dry wall board.

When hanging the drywall use drywall adhesive. Apply adhesive to the studs and hang the drywall with enough screws to hold it in place until the adhesive sets. After adhesive sets remove the screws holding the drywall. Screws transmit sound. 

Another thing that may be possible for the drywall is use a drywall designed for plaster coating. I think they called it blue board. I think plaster is somewhat of a sound barrier.

Check your supplier to see if they have sound proof doors. May need to build a special jamb for thickness of the wall. Eliminate the gap under the door using what may be reccommended.

Electrical outlets will have gaps without consideration for sealing the gaps. Check the net for ideas.