"If I want to print my own CD covers to make custom album art for a CD case, what is the CD cover size I need to use?"
The dimensions for a CD Cover are 12cm x 12 cm (4 3/4 inches x 4 3/4 inches). While you can certainly line this up yourself on a printer and then cut out your CD cover, it's far easier to use software that lines everything up for you.
I'm a longtime fan of the Acoustica software products. So far they've never steered me wrong. The CD and DVD label making software they offer is no exception. In addition to making a CD cover of the correct size, you can make the inset that goes in the back of the jewel case. You can also make a label to stick on the front of the disk or use HP Lightscribe technology to print directly on the disk.
I prefer to use printable CDs with a white surface that can be printed in a specially designed printer. Occasionally the stick-on labels are known to gum up the works in CD drives, so printing on the surface solves that problem. Before you get to far down the path of creating your CD cover, download Acoustica CD/DVD Label Maker and save yourself a headache.