Measure the chair and cushion, using a tape measure. You should measure and write down the length of the inside back, outside back, inside and front of arms --- double this amount --- outside arms --- double this amount --- seat and the front of the chair. The cushion measurements include the top, bottom and sides, all of which should be doubled. Add 2 inches to each of these measurements for a 1-inch seam, and you've got the total amount of required yardage.
Draw a scaled-down version of each of the chair's surfaces, using graph paper. This will serve as a rough pattern for you to follow.
Measure and mark the wrong side of the fabric, using a washable marker and following your graph paper guidelines. Label each piece as you go so you know how to sew them back together.
Cut out the fabric and pin the corresponding pieces together. The simplest way to do this is to lay the pieces on your chair right-side out and vertically pin the seams to the proper tension.
Iron the pinned seams to create a crease, and fold these seams backward so the fabric is now wrong-side out.
Sew along these reverse creases, using a zigzag stitch for good reinforcing.
Sew the cushion cover in the same way. Place a zipper at the back of the cover by pinning it in place on the pressed back edge and sewing it down with a straight stitch. If you are unfamiliar with zipper installation techniques, please refer to the Resources section of this article.
Turn everything right-side out and place it over the old chair.
Adjust the bottom line of the slip cover and create the desired hem, using a straight stitch. The hem should ideally be no deeper than 1 inch, so be sure to trim away any excess fabric.