Flatten the CD by gently pressing the broken edges together so that they are aligned.
Put a paper towel or soft lint-free cloth on a flat surface and lay the CD on top of it, readable side down.
Peel off a CD label -- available from print shops or over the Internet -- and remove the backing so that the adhesive part is exposed.
Make sure the crack in the CD is still aligned. Carefully align the adhesive label with the non-readable side of the CD and gently affix the label to the break. Rub the label gently to smooth it and ensure it has stuck well.
Dampen a clean, lint-free cloth with a bit of scratch remover fluid and wipe the readable side of the CD with the cloth in a linear motion from the middle to the edge. Apply the fluid particularly to the cracked area. Dry the CD with a clean, dry lint-free cloth.