So far, I've been doing this:
1. A blast from can of compressed gas.
2. A very light brushing with a large natural bristle brush, that dislodges dust and such, possibly followed by 1. above.
3. If still not clean, spray the screen with tap water from a fine mist button-top sprayer. I should probably use distilled water, don't know. Hey, how dirty can tap water be? Then, very lightly swab with circular motion with the cleaning cloth that came with my Nanao 17" CRT some ten years ago. I clean this cloth occasionally with soap and water.