You're already probably warm enough to know what I'm going to reveal as my method of cleaning my electronic screens. Yep, that's a picture of a pile of Microfiber Cloths. These microfiber cloths of mine pictured above are approximately 25% of the box that I purchased on Amazon. They were just under $23 with free shipping and I seriously think that this is all of microfiber I will need for maybe a decade; They're washable.
Once you have your very own microfiber cloth in your possession (don't I make that sound nice ;), you'll only need one more thing: Filtered water (I prefer any non-mineral type water), so that you're not worrying about any residue after a good screen wipe. Maybe it's just me, but when I think of well water, or any water that doesn't have a good chlorine filter on it, I picture calcium and other deposit buildups (who knows what's in your city or well water).
When I apply the water to the microfiber cloth, I approximately use only a couple tablespoon's worth. Be sure to pour the water very slow. I say this with caution because often, even though microfiber can absorb many times it's size, it takes long to do so; The water will splash right off and shoot in another direction if you pour it too quickly.
Next, gently take the wetter part of your microfiber cloth and wipe your screen. I've read many cleaning guides over the years and they often inform one to wipe in a circle. I personally find it much, much better to wipe in a straight path (think of squeegeeing). Why lose track of where the dust is at? I have attached a video to show you my results. I will admit this is not optimal quality as I'm holding a recording device in one hand and screen cleaning with the other.