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of the 3 videos I saw for cleaning screens, the distilled water method seems the best. I have read before that because of anti-glare and other coatings on the lcd screens. think:how would you clean expensive sunglasses with UV Coatings etc?
for best safety, for monitors, tablets (any LCD/"LED" screen), and phones I would recommend Distilled water only, and a lint-free cloth (like a microfiber cloth) like the 3rd guy says, and a spray bottle. wipe the screen gently.
avoid using thumbnails too much on monitors, that can leave a permanent smudge on the monitor. avoid using fingernails if you can at all.
never press very hard on the screen. it's a very thin glass. there are tiny transistors under the glass that can break, and you could have permanent issues with your display.
if you just use a wet [microfiber] cloth alone to clean the screen you will get dirt wiped around in the pattern of the path of your hand. it's not desirable because the dust will still be on the screen despite the wet-wiping. get the majority of the junk off first and deal with the minor stuff later with your wet cloth.
I have not had so much a problem with scratching with dust as some have said. but my stuff is not big and expensive and I don't know what those displays are like, mine is cheap. I can't tell if the display got scratched by dust because of the uneven surface of LCD monitors. I think 2 of mine are expensive old monitors or something. I notice no real difference, and they don't "scratch".