Well, if you insist on the rule being simple, here you are:
- a = some, any
- the = this, that
Two simple examples. Note that you just wrote "...if a person knows which item you are talking about...". You didn't write "...if the person knows...". And that's correct, because you are not pointing to this or that person, you are talking about any person in general.
On the other hand, my answer starts with "if you insist on the rule being simple". That's because you asked for a rule (= any rule), and I am now talking about that rule. We are talking about the same thing.
Now, I can't think of a (= any) simple rule of thumb when not to use an (= any) article at all, but here are some suggestions:
- Don't put an (= any) article before a (= any) noun if the (= that) noun is preceded by:
- a number
- a possessive adjective ("my", "his", "our"...)
- a "no", "some" or "any"
- a "this", "that", "these" or "those"
- Give me a chair! (= any chair you like)
- Give me the chair! (= this chair)
- Give me that chair! (no article, you already specified which chair you mean)
- Give me my chair! (no article)
- Give me five chairs! (no article)
- Give me some chairs! (no article)
- Give me the chairs! (= these chairs)
- Give me these chairs! (no article)
- Give me a reason to hit you! (= any reason will do)
- Give me no reason to hit you! (no article because of "no")
- Give me no reason to hit you with a chair! (= any chair)
- Give me no reason to hit you with the chair! (= this chair)