What would you recommend to clean the surfae of the cel? What about the paint side. I notice that some cels tend not to be clear plastic but almost have dingy/areas without color- but just seem to have something on it (hard to explain). I noticed in Sensei's text he cleaned a cel to discover his treasure.
Does it need to be done professionally or can a layman do something?
I think the cel you mean was just one that had gotten so dusty in transit that it was hard to appreciate its condition until I'd gotten it properly clear of the loose dirt. That's simple: distilled water (tap water will dry and leave spots) and a soft, clean cloth.
But I think what you're referring to might be what some collectors call "oxidation." That is impossible to remove, unfortunately, as it's a degradation of the plastic itself. I don't know what causes this, but I'd guess a combination of using a cheap grade of acetate and exposure to light. About all you can do is to scan/display the image against a background that doesn't call attention to it and keep it in complete darkness when it's not being looked at, as with any piece of animation art.
Perhaps other collectors with better knowledge of archival techniques can chime in, but I've never used anything stronger than the above to clean cels. I know that anything that is alcohol-based (like many "waterless" cleaning cloths) will dissolve cel paint and trace lines and so should never be considered.