Here it is.
Every: Only used before singular count nouns.
I own every book by Margaret Atwood. This means that I have all the books written by Margaret Atwood.
Any: When used in a sentence, use the negative. You can use it with count nouns (singular and plural) and non-count nouns.
I don't own any books by John Grisham. (plural count noun)
I don't have any idea why someone would cheer for the Toronto Maple Leafs. (singular count noun)
I don't have any coffee. (non-count noun)
One thing I'd like to point out is even though you have to use a negative sentence structure with ANY, the meaning itself can be positive.
I don't have any symptoms of AIDS. (This is a good thing)
In question format, ANY is interchangeable with SOME, although using ANY is more familiar and common.
Do you have some coffee? (good)
Do you have any coffee? (good+)
I hope this answers everyone's questions. If not, please leave a comment or contact me.