Lay the CD on a flat clean surface with the face that you want to see when you are using it as a coaster down. Make sure that the surface that is up is clean and dry.
(You may want to wipe it with a soft cloth)

Peel back and fold over about one third of the backing material on the large cork disk to expose the pressure sensative adhesive.

Using very little pressure, position the cork disk, adhesive side down, on the CD so that it is centered. Once you are satisfied with the position, firmly press the third with the exposed adhesive against the disk to bond to the CD.

Lift the edge that still has the backing on it, grasp the edge of the folded over backing, remove the rest of the backing while pressing the cork firmly against the CD working out towards the edges.

Okay, you're almost there. Turn the CD over, remove one of the small cork disks from it's backing and place it, adhesive down, in the center of the spindle hole on the CD. Press into place.
(you might want to use a straight pin, or push pin stuck into the cork to aid in positioning it)

This step is optional but advisable. Remove one of the stylish waterproof labels from it's backing and place it over the center of the CD. This will seal the cork in the spindle hole against moisture, stains, and other undesirable crud that might detract from your spiffy new coaster.

Now, wasn't that easy? You have successfully recycled/repurposed an otherwise useless CD. Don't you feel good about yourself?
You should - YOU ROCK!