How do you know the operating system is damaged?  

Typically you'll know.  The dreaded Blue screen of death is one way you'll know.  Registry errors or text screens displaying at boot up with warnings about damaged files or missing files may be your clue.  When a computer will not boot up for you, that is usually a the bad indication that you have a damaged operating system.  Always try to boot into Safe Mode as part of your diagnostics.  How to boot into Safe Mode.

Using the Operating System CD

In most cases, you would start by popping in the operating system CD-ROM that came with your computer and boot the system up.  When prompted if you want to boot from the CD ROM, confirm Yes, that you do.

Operating system installation disks can differ widely so it's difficult to cover how you may be prompted.  What you are looking for is options to "Repair" or re-install the operating system files.

BE Aware ... Some "recovery" disks provided by computer manufacturers will actually do a RESTORE of the computer back to it's original state when it was new.  That mean ALL of your files, programs and data will be wiped from the computer!  Be aware.  Read all of the labeling and warnings if continuing along with the installation disk.  Also be aware that mny tech support persons will be far too quick to recommend this as your ONLY option.  Use this option as a LAST resort.  Always backup your data routinely just in case you have to resort to the dreaded system restore.