I feel like I have seen commas both inside and outside of quotes in major publications.
Do commas always go inside a quotation mark?
In America, commas go inside the quotation mark (except as stated below, when the question is not part of the quote, it goes outside the quotation mark).
However, in the UK, commas, question marks, etc. all go outside the quotation marks. As always, you need to know your audience!
In the United States, generally speaking, you'll be using MLA Style when writing English papers. This is the style set forth by the Modern Languages Association. It says: "Commas and periods that directly follow quotations go inside the closing quotation marks." Question marks, however, are often handled differently. If the question is part of the quote, the mark goes inside the quotation marks. If the question is not part of the quote, it goes outside.
In journalism, the default style guide is AP style. This is the style set forth by the Associated Press. All punctuation goes inside the closing quotation marks.
Students studying for the GED Language Arts test know that tricky questions include comma and quotation mark usage. The general rule is that commas and periods are placed inside the quotation marks; other punctuation marks are placed outside IF not part of the original quote. A comma is used between a direct quotation and a preceding or following clause, while no comma is used before a quotation that is integrated into the sentence. i.e. The new spa's advertisement promotes "a healthier life style."
Commas and periods always go inside the quotation marks. Question marks and exclamation marks are place according to the sentence in question. If the question is part of the quote then the question mark goes inside the quotes, if the question is about the quote the question mark is placed outside the quotes.
For the most part, commas always go inside quotation marks, especially when you're directly quoting something that someone said, such as, "Mom, I don't want to go to the park," said Lou.
I hope this helps!
I teach all of my students to put all commas and punctuation inside the quotation marks. I've heard that sometimes very specific formatting requirements will place punctuation on the outside, but I have never seen than myself. When in doubt, keep it all on the inside!