Some things vary more than others. In the United States, the tradition is to have periods (or full stops) inside quotation marks (or inverted commas), for reasons that have more to with old-style hand typesetting and tradition than anything else. However, other situations are a bit more clear. All other punctuation (including full stops and commas outside the U.S.) follows the rule that if the punctuation belongs to the quote, it goes inside, and it goes outside otherwise. Which makes sense. Exceptions to the general rule are rare and tend to deal with legal documents and things like that.
The little trick to this is that if there is a full sentence in the quote, you might believe that you need two marks, one to end the quotation, and another to end the sentence it’s embedded in. This is usually frowned upon. You usually will see two periods reduced to one (which would go outside the quote, except in the U.S.), a period and a question mark or a period with an exclamation point reduced to a question mark (placed according to the rules. A question mark and an exclamation point are the exceptions, you would probably use both, or you could get rid of the exclamation point since it’s easily done away with. Some examples:
U.S.
She called me and said, “I’ll be a bit late.”
She called me and said, “I’ll be a bit late,” and then she hung up.
Elsewhere
She called me and said, ‘I’ll be a bit late’.
She called me and said, ‘I’ll be a bit late’, and then she hung up.
More or less everywhere (except for “ ” vs. ‘ ’)
I think she said, “When will you be there?”
Did she say, “We’ll be there at eight”?
I think she said, “I can’t wait to see you!”
I can’t believe she said, “I can’t find my keys”!
U.S.
Did she say, “We’ll be there at nine?” or did she say, “We’ll be there at five?”
She either said, “I can’t wait to see you!” or she said, “I don’t want to see you!”
(No comma after the end of the first quotation)
Elsewhere
Did she say, ‘We’ll be there at nine?’, or did she say, ‘We’ll be there at five?”
She either said, ‘I can’t wait to see you!’, or she said, ‘I don’t want to see you!’
More or less everywhere (except for “ ” vs. ‘ ’)
Did she say, “I can’t wait to see you!”?
I can’t believe she said, “Are you going to wear that?”!
(Losing the exclamation point and following the general rule would work here, too.)
And so, with my incredible ability to write convincing dialogue well on display, you would probably want to write,
What do you think of the advert where the bear says, ‘It’s the creamiest chocolate around’?