*Note: The following applies to CM1 games only (PC) and does NOT apply to the Retail Special Edition version.*
Create a directory somewhere on your computer called "CMBO" (Recommend C:\Program Files\CMBO). Now open Windows Explorer and browse to the Combat Mission CD. Copy the Wav, BMP and Scenarios folders into your new CMBO folder. Be sure that you copy the folder AND files inside of them! Now copy the Combat Mission.exe file from the CD to your new CMBO folder.
Now launch the game from your hard drive. You will still need to have the CD in the CD drive to play the game (this is done for copy protection reasons) but all the files will be on your computer and it should be okay.
Make sure to also [check out this knowledgebase entry] if your CD contents are different!