Remove the staples or tacks from the furniture with the needle-nosed pliers or by prying them off with a screwdriver. As you do so, keep in mind how the fabric was affixed to the furniture so you can replicate the process when putting on the new fabric. Make a note of where the fabric was attached to the frame.
Smooth out any lumps in the padding with your hands. It is not necessary to remove the padding; you can put your new fabric right over it.
Use the upholstery that you removed from the furniture as a pattern to cut out a new piece. Lay your new material out on a table or on the floor. Place the old piece of fabric on top of the new and pin them together with straight pins.
Use the fabric shears to cut the new fabric in the shape of the old fabric, but add one inch all the way around so that the new piece of fabric is one inch larger on all sides.
Lay the new fabric over the back of the furniture and tuck it in around the sides. Hold the fabric taut as you staple it to the underneath of the furniture frame with the staple gun. Cover the sides of the furniture doing the same.
To cover the arms, fold a third of the fabric, the end that's adjacent to the back, forward. Pull the fabric on each side of the arm tight and staple it to the frame. Cut a slit in the middle of the fold and wrap the two sides tightly around the arm and staple it to the wood frame with the staple gun. Do the same on the opposite arm.
Pull the fabric taut over the seat and staple it to the front underside of the frame with the staple gun.