I plan to do a couple more in other basic colors, to have a nice set to kick around the living room.
Step 1: Materials
Step 2: Panels
Grab two of the panels, place the good sides together, and sew one of the edges using a straight stitch.
For the first five seams, sew all the way across the long edge. For the last seam, only sew from the ends to a few inches towards the center. You want to leave enough of a hole to fit the arm of the sewing machine in to finish the ends as described in the next step. Also, you want to be able to have an opening to put the stuffing!
Step 3: Ends
Cut out two circles using a cup (or anything else round). Pin the circles on the outside of the ball, then sew with a straight stitch around the circle to attach it to the ball.
Clean up the edges of the circle by switching to a zig-zag stitch, and sew around the very edge of the circle. You could skip this step if you really want to, but it makes the final product look much cleaner.
Step 4: Stuffing
When you are satisfied with the amount of stuffing, hand-stitch the last seem closed. I went with a whip-stitch, and just went across and back to finish right where I started stitching.
Depending on the fabric you use, your finished ball should be machine washable. It will probably take a while to dry though, especially if you went with a lot of stuffing.