Remove the fabric from the patio cushion by ripping the seams open with scissors or a seam ripper. Avoid destroying the fabric so that you can use it to make a pattern for the new cover.
Clip open the remaining seams and lay out each piece of fabric on a piece of paper. Trace around the pieces with a pencil to create a paper pattern. Add 1/2-inch seam allowances around each piece if you cut seams off while removing the cover.
Pin the paper pattern pieces to new fabric of your choice. Cut out each pattern piece with fabric scissors.
Pin the covering pieces with right sides together, following the layout of the original covering. Stitch the pieces together, using a 1/2-inch seam. Leave one side seam open.
Insert the foam cushion through the open seam. Fold the material under 1/2 inch from each side of the opening, and pin or iron them. Pin the folded edges of the opening together, and stitch it closed with a running stitch.