Line the tops and sides of any doors in the room with weather-stripping foam tape. Press the tape firmly down around the perimeter, then close and open the door several times to ensure it doesn't stick and that it closes properly.
Replace hollow doors with solid core doors. Install a door sweep on the bottom of any door in the room. The sweep should just brush the floor. This reduces the space between the door and floor, limiting how much noise travels outside the band's rehearsal area.
Place a 1-to-2-inch foam, rubber pad on the floor before your son's instruments and equipment. Know that bass from the drums and lower frequencies are more difficult to insulate than higher frequencies.
Lay down mass-loaded vinyl over the foam if you're willing to invest more money in reducing the band's noise. Place two layers of the vinyl at right angles to each other so the sound doesn't travel through seams in the strips.
Place equipment that shakes, like speakers or instruments, on vibration-isolation pads.
Hang sheetrock panels from your ceiling with furring channels. This false ceiling creates a dead-air space that traps sound.