Decide how you want to replace the cushion fabric. Often if you know the manufacturer of the furniture and the furniture is not more than several years old, the fabric may be obtained directly from the manufacturer. If this isn't possible, the next best solution is to find a fabric that complements the existing fabric of the furniture. Take a sample of the existing fabric to a fabric store and find some fabric that appeals to you. Buy several yards of fabric.
Remove the fabric covering from the damaged cushion carefully. Rip out the seams with a seam ripper to preserve the cushion cover. Use this preserved cover to make a pattern to recover the cushion. Lay the damaged cushion cover out, and with a fabric pen trace an outline of the cover onto the wrong side of the new fabric. Add a 1/2-inch seam allowance along all edges.
Carefully cut out the newly-traced pattern from the fabric.
Sew the new cushion cover with a sewing machine. Follow the existing cushion pattern and sew three sides together. Press the seams and turn the cushion cover right-side out. Pull out each corner to a sharp point.
Place the old cushion into the new cover. Slip-stitch the open edge shut with small, even stitches.