If you're attempting to make a CD cover without the use of third-party software, the first thing you should do is take measurements of your CD's case. Each type of CD case will be shaped just a little bit differently, so take a tape measure or ruler and measure all sides of the case so you know how big of a space you have to work with. Measure accurately to ensure your CD cover will fit properly in its new home.
Next, use a photo editing program that will allow you to create a new image from the ground up to design your CD cover. Input the exact measurements of your CD case so you design the image to the right size. You can include images you found on the Web, or design your own. There are many programs you can purchase to edit images on your computer, but a free program you can use for this kind of work comes with all Windows-based computers called MS Paint. It is accessible through the "Programs" menu.
Most professionally-made CD covers are done on high-quality paper from high-quality printers. If you don't have these options available to you, the next best thing is to go to a local print shop like Kinko's. You can take your finished CD cover into a print shop on a CD-ROM or flash drive and they can print it out for you on high-quality photo paper very cheaply. All you have to do after that is cut it out of the paper and slip it into your CD case.