Look for microscopic scratches (hairlines) (sometimes not so microscopic) that catch the light, or a "flat" look where the natural frosty luster is gone, losing the original "cartwheel" effect of an original coin. Comparing it to an uncleaned coin is often the best method. This is when a loupe and a strong light are useful.
I don't mind gently cleaned coins - it can be done carefully with little to no damage. OTOH, sometimes for some coins I've happily bought more heavily cleaned ones because that brings the price down to a level my budget can afford. As an example I have a cleaned 1873 Bordeaux mint 5 Francs coin that is XF/AU details. Without cleaning, it goes for $125+; I got the cleaned one for $45 - less than melt. I'd love to find, for example, a cleaned but otherwise nice 1905 shilling because they tend to be quite expensive as _the_ key date in the 20th century. A cleaned one that is otherwise nice might have a price tag my budget allows more easily.
Some collectors won't touch them at all but only really harsh cleaning with scratches and totally destroyed luster are the ones I avoid.
Hope this helps.