Can you explain to me, in plain language, when to use plural and singular after "any"?

I think my education failed me on this one.

I have memory of being taught that nouns after “any” should be singular. But as time went on, I realized that I saw plural nouns more often than I expected. Sometimes it’s singular and sometimes it’s plural. It just seems to me that the noun just changes whenever it wants to and there is just no rule. Can anyone help me understand this?