This monitor is a ***** to clean properly. Glossy and no glass, not good if you have OCD.
I use a clean Apple microfiber cloth, with a very tiny bit of water. Make sure to wash your hands too, or the oils on your fingers will go through the damp cloth leaving streaks on the screen. Circular movements are better than straight ones. Don't press too hard, there is no glass protecting the screen.
I don't use any cleaning products, learned my lesson after using one on an iMac glass screen - resulting in huge streaks than wouldn't come off no matter how much I rubbed. Took me 2 hours to get rid of them.
I clean mine every 6 months or so - for normal dusting I use a Pledge/Pronto fluffy duster.
Edit: make sure you dust it first before using a cloth on it, or the dust particles will act like sandpaper and potentially damage the screen.