All you need to do is slip the pillowcase over the chair, leave it be, tuck the excess under, or add a ribbon embellishment to hold it into place. Instant decorating at its best!!!
You can find all sorts of pillowcase sets at retailer's like Marshalls, Home Goods, TjMaxx, and Ross for a few dollars a pair.
Iron the wrinkles out and then just slip the pillowcase over your chair. Depending on the height of your chair and the length of the pillowcase, you may have bunched up fabric at the bottom.
You can leave it be or tuck the excess fabric under.
Tie a ribbon around the chair and tie into a bow on the back.