Put on gloves and a dust mask. Pull out the old insulation by hand, stuffing it into plastic bags. Vacuum the area of any residual dust and loose insulation.
Measure the height of the wall along one of the studs. Roll out fiberglass insulation on the floor. Lay out the tape measure alongside the insulation to the length that you took from the wall.
Lay a square across the piece of insulation. Cut across the width of the insulation by running a razor knife next to the square.
Press the insulation into the space between the first two studs, filling the space completely from top to bottom. The paper-covered side should face out into the room.
Attach the piece of insulation to the studs, shooting staples through the sides of the paper backing and into the studs. Put staples about every foot up and down the length of the studs.
Cut out the insulation around electrical boxes and other obstructions with the razor knife. Repeat the process for each space between each pair of studs. When you install new drywall, affix it to the stud edges over the insulation.