How does a hash table work?

I’m looking for an explanation of how a hash table works – in plain English for a simpleton like me!

For example, I know it takes the key, calculates the hash (I am looking for an explanation how) and then performs some kind of modulo to work out where it lies in the array where the value is stored, but that’s where my knowledge stops.

Could anyone clarify the process?

Edit: I’m not asking specifically about how hash codes are calculated, but a general overview of how a hash table works.

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