i haven't dealt with this in a long ass time, but just a couple of quick questions. what OS are you running (windows? something else?) and i'm assuming it's like some kind of burned/written CD with a typical data structure like folders with files, etc? not an audio or video cd, right?
EDIT: gonna assume windows and a data CD, and you're just trying to like open it / drag and drop from windows explorer. basically, the intuitive first start. don't panic. that method works if everything is perfect, but if the disc is old and has some physical (even minor), basic software like windows explorer will just stop and throw critical errors rather than attempt to read non-perfect sectors. OS internal software is a precious princess when it comes to wonky physical media. which is fine. it's like a maserati, and instead of high octane gas, you've got some kerosene that you found in a shed with some water on top. you want a shitty old workhorse engine that will make heat from trash juice.
so you want specialized software for this. the windows based recommendation that seems to be still around is called TestDisk which i believe works across all kinds of physical media (CD/DVD/internal & external drives, partitions, etc).
here's some general information that has a lot of info about what to expect in the process, bonus in that it provides software recs for linux users!
spoiler alert: (it takes a long time to recover data with disk utilities). so you'll run a utility to extract and build a disk image file on your machine (probably a .iso) and then you'll use disc imaging software to "mount" that as a virtual drive, and then you should be able to browse it and get what you want off it.