In the walls, put R-30 insulation between the studs of the interior walls. Also, make sure all holes are well sealed (around outlets, door...) Doing these things will eliminate most of the sound - the high and midrange frequencies.
The low-end frequencies (does he listen to a lot of hiphop/rapcore with the bass turned way up?) can be reduced by limiting the amount of contact - uhhh how do I say it? ... Fir out the walls with 1x2 (across the studs) - that will mean that the drywall only contacts the studs where the firring strips contact the studs - making fewer points of contact that pass all the way from the inside of the room to the outside. If I think of a better way to describe it, I'll post again.