Adding to @LaurenIpsum: Keep in mind that different countries punctuate differently. From this source:
American style uses double quotes (“) for initial quotations, then
single quotes (‘) for quotations within the initial quotation.
“Economic systems,” according to Professor White, “are an inevitable
byproduct of civilization, and are, as John Doe said, ‘with us whether
we want them or not.’”
British style uses single quotes (‘) for initial quotations, then
double quotes (“) for quotations within the initial quotation.
‘Economic systems’, according to Professor White, ‘are an inevitable
byproduct of civilization, and are, as John Doe said, “with us whether
we want them or not”’.
The above examples also show that the American style places commas and
periods inside the quotation marks, even if they are not in the
original material. British style (more sensibly) places unquoted
periods and commas outside the quotation marks. For all other
punctuation, the British and American styles are in agreement: unless
the punctuation is part of the quoted material, it goes outside the
quotation marks.
However, this site disagrees with the above site on some details. But, it agrees with me on the illogic of both systems.
The question of whether to place other punctuation marks inside or
outside quotation marks is a controversial one, [with] both the British and
American practices being to some extent at variance with logic. The
rule would seem obvious: other punctuation marks appear inside the
quotation marks when they are part of the quotation itself, and
outside when they are not. It is one of life’s enduring mysteries,
however, why neither British nor American conventions follows this
simple principle.
My advice is to be logical and consistent. If an editor insists on an illogical reformat ("because that's the rule"), then threaten to drop quote marks altogether, as some authors have done. :-)