Keep your CD-ROM in its plastic jewel case when you are not using it. Never touch the shiny silver side of your CD-ROM. Handle it by the edges only.
With proper care, your disk will probably never require cleaning. However, if dirt, dust or finger marks should appear on your disk, gently clean it with a clean, dry lint-free cloth by wiping from the central hole out towards the edge in a straight line. Never wipe with a circular motion, because if you did create a small scratch it would be far more likely to make the disk unreadable.
Never use water, detergents or abrasives on your disks. If necessary, you can use an alcohol-based cleaning fluid to clean them. There are CD cleaning kits available from most record shops to help you clean your disks.