Cut two pieces of fabric 1 inch larger than the dimensions you're planning for your pillow (to allow for 1/2-inch seams), using scissors.
Place the two pieces of fabric face to face. Trim as necessary if they're not the same size.
Pin the two pieces of fabric together on all four sides.
Sew three sides together with a 1/2-inch seam, hand-sewing with a needle and thread or using a sewing machine. If you are making a cover for an existing pillow, leave the fourth side open. If you are stuffing a new pillow, sew the fourth side and leave 2 or 3 inches unsewn to allow stuffing.
Trim the corners with scissors to remove excess fabric and turn the pillow inside-out.
Insert the existing pillow or fill the pillow with stuffing to the desired firmness.
Sew the opening shut, using a slip-stitch.