One of the great advantages that CD and DVD drives have over old style magnetic media is that they generally don't have to be cleaned. Tape drives and floppy drives required occasional cleaning since the heads that read the media also touched the media. In CDs and DVDs the media is read by a laser and nothing touiches the disk. In theory.

Hard disks are entirely sealed and so never need cleaning.

Since optical disks are inserted into a drive it's possible for them to carry contaminants into the drive and you may have to clean some of those away.

We were remodeling out house and had a few issues with the dust created. Our Playstation game machine, which has a CD bay that opens with a pop-up lid, suffered from the dust.

Computer drives are much better protected. If you're getting read errors my suggestions is to carefully look at the disk itself. Fingerprints and dust won't ruin the disk, but they may make it hard for the computer to read.

Whenever we've had an issue with a computer drive it turned out to be a dirty disk, not a dirty drive. Still a drive can get dirty and a dirty lens won't let the laser properly read the disk.

The drive itself can be taken apart to be cleaned, but that's requires a lot of time and care and you really have to be careful. It's easy to kill the drive, so I don't recommend that.

A can of compressed air, specifically made for computers, can be found at any computer store and most office stores. These can be used to blow dust out of drives, as well as clean dust off of delicate electronics.

To clean the drive you can get a drive cleaning kit from Amazon or any other computer store and probably from those office stores as well. Just follow the directions on the kit and you'll be fine.

As for the disk itself, you can duy a disk cleaning kit or you can clean them like you'd clean your glasses. Use a very soft tissue and clean water. Don't use chemicals as they might damage the disk.