Yeah, you just need two pieces of wood and three dowels per row of CDs. For a small rack you can get away with smaller diameter dowel stock, but go with like 3/4" if the racks are wider than a couple of feet. Otherwise they'll sag and your CDs will slide toward the middle after a while. 
Use something like tung oil on the dowels. You just want to lightly apply it to seal it and keep out dirt and stuff. If you put a thick finish or paint on the dowels your CD cases will tend to stick to it.
The sides ...
I didn't use any wood at all for the shelves, only for the uprights. I only used 2 dowels per shelf.....both underneath the cd's...rear one just a bit lower to prevent fallout. Since I hung mine on the wall, the back is completely open....and the wall keeps cd's from falling through.
On the dowel sagging...
If shelves are not very wide it should be fine with just 2 vertical boards, one on each side. To test mine I just snapped everything together in a dry run (no glue) and filled up one of the shelves with cd's. It was sagging from the outset, so I knew that a vertical support in the middle was needed.
I hand sanded and used several coats of tung oil on everything. If you use attractive enough solid wood (in my case, red oak), that's all you need.
So the parts list is quite minimal:
2 (maybe 3) vertical supports
2 dowels per shelf
glue
sandpaper
tungoil, or other finishing product
L brackets for hanging.
Measure accurately, cut, drill and assemble squarely, and you are set.