Many household cleaners can damage the protective coating of the monitor and should not be used.  In particular, Ammonia-based cleaners should be avoided.  A good quality microfiber cloth (dry) should be used for cleaning when possible.  Use light pressure to gently clean the surface of the monitor.

If the dry microfiber cloth is not sufficient, lightly dampen the microfiber cloth with distilled water.  (Tap water may contain minerals that cause smearing or discoloration.)  Again, use light pressure to gently clean the surface of the monitor.

If more aggressive cleaning is required, a 50/50 solution of distilled water and isopropyl alcohol may be used.  (Do not use rubbing alcohol, 70% or greater isopropyl alcohol only.)  Mix an equal amount of distilled water and isopropyl alcohol.  Lightly dampen the microfiber cloth with the solution.  Again, use light pressure to gently clean the surface of the monitor.