It all depends. If the comma or the period are part of the sentence inside the quotation marks, they should remain inside. Same for all other punctuation maks pertaining to the quoted sentence.

Example:
>> He told me: "Did you take the books, bags and the map?"

All punctuation marks are kept inside the quotation as part of the original sentence.

Here's
'A Functional Guide to Some Problems of English Punctuation'
for general reference to anyone interested.

http://www.hum.au.dk/engelsk/pages/punctuation.shtml

From the introduction:
-Most guides to punctuation usage are organised under the different punctuation marks. Thus, you can look under 'commas' and find ten different uses of the comma listed, and so on. This is fine if you want to make a full list of all the different things punctuation can do in English. However, it is not so convenient if you have an idea of what you want to do, but don't know which punctuation mark - if any - should be used.

-This guide is organised according to the functions of punctuation, the different things that punctuation can be used for. Hopefully, it will be useful for looking up the solution to specific problems. It is not intended as a systematic and complete account of English punctuation, but concentrates on areas of punctuation use that often cause difficulty.

-Both British and American systems of punctuation are described in cases where these differ.

In BrE, I was always taught to put a comma before the start of the speech, and that punctuation required within the speech always went inside the speech marks.

hth

Marion asked "Why?"
Have you seen "About a Boy"?
"I'm going to get him back," he said angrily.
He said angrily, "I'm going to get him back."