Seal off any leaks around windows with caulking. If the window is single paned, either replace with a double-paned window or hang heavy curtains in front of the window. The curtains will absorb some of the noise in the room.
Run a stud finder across the wall and mark the studs. Cut a 2-inch diameter hole in the center of each wall cavity between the studs, roughly 8 inches from the ceiling and pump in cellulose insulation. Patch the holes and repaint the wall.
Add an extra layer of drywall to the wall and ceiling if insulating is not enough. The drywall can be directly attached to the studs using drywall screws. You can then add texture and paint the walls.