Is it coated? Do you have any instructions that came with the monitor that might address this? If so, follow those. Most CRTs are glass or coated glass. Regular glass cleaners using a soft cloth without rubbing will usually work fine. Some camera lens cleaners might also be good to take away small fingerprints. Again...soft cloth such as for use on glasses or lenses should be ok. Avoid strong solvents, of course, and stick with mild surfactants where grease and oil are a problem. Maybe some coaching for your daughter might help if she's old enough to understand.
what can i get to clean the fingerprints off my computer screen? my daughter always touches it.