Sega Saturn Modchip
If you want a pain free way of playing CDr discs on your Saturn, then I think the easiest way is to install a modchip.
If your Saturn has a CD drive that attaches to the motherboard with a 21 pin cable, then you're in luck, there's a few shops selling a suitable modchip and they usually provide excellent online guides for installing it.
If you have a CD drive that attaches using a 20 pin cable (Model 1 Saturns with oval buttons, and some very early Model 2's I think), then it's a lot more difficult. I haven't seen a suitable chip for sale for years. You can mod your modchip though!
Here's the best guide I've seen for it, along with some more info. Here's a PDF copy of the original guide should Sega Style ever vanish,
This chip would be a nice find though!
Thanks jeimuzu_uk for finding some of the links for me :-)