When is the "h" pronounced?

I have recently become better acquainted with a lady at church for whom English is not her first language. She mentioned the difficulty in knowing whether to pronounce the "h" in English words - sometimes it is silent. I had not even thought about this before (I would have thought it may have come up in ESL, but I don't remember it).

Read through these, is the "h" sounded or is it not?

• honor
• humility
• have
• hope
• hover
• hand
• hour
• how
• hospital

There are other examples when the "h" is not the first letter: ghost, rhythm, exhausted.
And one of the websites mentioned that there are words where the "h" is pronounced when the word is emphasized, but not when it is unemphasized, like "his" - "It isn't mine, it is *his* book." versus "We are going to read from his book." (saying it casually rather than emphasizing)

As a native English speaker, we just "know" how a word is pronounced, and we know how to spell it even if the "h" is not sounded... it does not appear that there is a good rule to follow with regard to this!

Some websites for further study:
https://en.oxforddictionaries.com/explore/words-with-silent-h/
https://theaccentsway.com/the-h/
https://jakubmarian.com/list-of-words-with-a-silent-h-in-english/

I think I'm glad I learned English as my first language, though I really wish I was fluent in some other languages as well!