Where to place a period?
First, it's important to know that American and British punctuation are different. For a very long time, the majority of Americans have followed very strict rules regarding periods and commas: always put them inside quotation marks.
Lucas the shark described his daughter as "a cut-throat lawyer in cards."
In July, Abigail and Lucas spent their honeymoon in Vegas, "gambling."
In British English, these same quotes would have the period moved to the outside:
Lucas the shark described his daughter as "a cut-throat lawyer in cards".
In July, Abigail and Lucas spent their honeymoon in Vegas, "gambling".
The distinction in British English is that the period should be outside the quotation marks if it is not part of the quote itself.
With the spread of the Internet, it's becoming more common for Americans to pick up British punctuation, especially in cases when the inclusion of the period inside the quotation marks could create confusion. I imagine that the British form will gradually replace the American, but that's only conjecture; for now, when writing for employers or schoolteachers, punctuate as appropriate to your geographic location.
Lucas circled "tall" and "handsome".
Lucas circled "tall" and "handsome."
What Lucas circled was probably not handsome-with-a-period. But on the American side of the Atlantic, the second example is technically correct. If your professors are American, use the second sentence.
If you work or go to school internationally, you'll want to use the former.
The one American exception seems to be (according to the Chicago Manual of Style, 16th ed.) in cases of websites, where including the period would change the website.
For a related but-not-quite-an-exception, if you are citing someone in a case where the parenthetical documentation accompanies a single sentence, the period will go after the parenthetical citation:
There were only fourteen snargleblasters on the planet "when Soup de Jour crashed and began his drive to recruit snargles" (The History of Snargleblast 87).
More on the subject of periods in relation to quotation marks can be found at:
Questions? Further exceptions? Which do you use, and why?