Hi I use a drop of methylated spirits in a saucer of warm water, and then use my wife's round make up remover cotton pads to clean the screen. Squueze excess water from the pad and then clean the screen, use 1 or 2 clean new cotton pads to wipe off any residue - dont worry if you leave a few smears they will dissapear once the water has evaporated. The metho seems to promote drying and evaporation.
I use the same method for window cleaning and shinny floor tiles - just put a squirt in a bucket and mop tiles. For widows use a cloth soaked in the mixture and then squeeze the cloth to remove excess water, clean the windows, get a car window wiper and remove residue and then use a leather cloth/micro fibre cloth to remove the last drops from the corners.
hey presto shinny clear windows, screens and floors for a few cents!