Which is the correct place to put the full stop (period) or comma when using brackets? Is it .) or ).

If the parenthetical statement is part of, and at the end of the sentence, then it is .). (Without the second period.) If the parenthetical is free-standing, as was my last, the period goes outside. That is my understanding in American English.

There are really four questions here, Storm - comma and full stop, inside or outside brackets.

For commas it all depends what is contained (in the brackets), and if (or, indeed, whether) the sentence stands up grammatically without the bracketed bits. My example is somewhat contrived, but I think shows that a comma is rarely needed within the brackets at the end of a bracketed piece.

A full stop should only come within a bracket if the bracket contains a full independent sentence. 'We normally see a clear sky as blue, because of refracted light. (In space, of course, there is no refraction and the sky is black.)'

I hope that is not too confusing!

I generally put comas and periods outside of parentheses (in this manner). (Unless the entire parenthetical sentence is standing alone, like so.) It just looks better (to me, anyway), that way.

Parentheses is a web page I knew I'd seen, but forgot to mention in my other answer. It says much the same as we have all been saying, but possibly a bit clearer.
Scroll down the page to 'Parentheses'.