There's a rule in American English that commas and periods should always go inside the quotation marks in quotes, even if they're not part of the thing being quoted. For example, suppose John said this sentence: "I read a book yesterday." Now suppose that John actually did not read a book yesterday, and the narrator wants to discredit this claim. Here's how that might look:

John said, "I read a book yesterday," but he was lying.

Even though John's actual quote ended with a period, the sentence within which it's framed necessitates a comma, and the comma goes within the quotation marks per the grammar rule.

This is a bad rule. The comma wasn't part of what John said, so to put the comma within the quotation marks misrepresents John. Here's a better way to write this line:

John said, "I read a book yesterday", but he was lying.

Here, the comma goes outside the quotation marks. It fills its purpose in the sentence without misrepresenting the quotation. I would even argue it's reasonable to write it this way:

John said, "I read a book yesterday.", but he was lying.

In this sentence, we are not truncating John's statement. The reader can see and understand that John's statement has reached its conclusion, and we're not representing only part of what he said. It's a little cumbersome, but it's more explicit.

When representing other people's statements as quotes, it's important to represent them exactly or be clear when changes have been made. As such, I place periods and commas outside quotation marks when appropriate. If you notice this in my writing, know that it is a deliberate choice.

I believe British English actually handles this rule properly, unlike this nonsense we have in American English.