Clearer sound after reconnecting cables?

The recommended way of cleaning them? There are more than one, which is typical of course.

The simple way is just to unplug them and then plug them back in. That will wipe some stuff off, probably enough to make a good contact again. Do it once a year when you clean out the rat's nest behind your system.

Another way to do it is more expensive. Use a contact cleaner and wipe the metal surfaces. Some cleaners also protect the surface from crud buildup. One of the most popular is Caig DeoxIT Gold.

To unplug and then plug back in does not clean anyhthing. It just moves stuff around.

As Tobias said, you can buy electrical contact cleaners such as Caig DeoxIt. DeoxIt Pro Gold is designed for cleaning gold connectors. I stopped using Caig products years ago because it leaves a film that can cause an ugly build up.

Radio Shack has electrical contact cleaners that do not leave a film, they just leave a clean surface. I have also tried some of the commercial cleaners with very good results.

I recommend Kontak electrical contact cleaner.

After you clean them, you might want to try using Stabilant 22. It is the active ingredient in what used to be called "Tweek". It is a bonified contact enhancer used in military, communications and IT fields.

It is made by the people at Dayton Wright of yore.