The following comes from the Purdue Online Writing Lab's MLA Formatting and Style Guide. Go here to check it out for their citation of the original MLA handbook.
If you add a word or words in a quotation, you should put brackets around the words to indicate that they are not part of the original text.
Jan Harold Brunvand, in an essay on urban legends, states: "some individuals [who retell urban legends] make a point of learning every rumor or tale" (78).
And here is corroboration from Doing Honest Work in College: How to prepare citations, avoid plagiarism, and achieve real academic success, by Charles Lipson:
ADDING WORDS [IN BRACKETS] TO CLARIFY A QUOTE
Occasionally, you need to add a word or two to clarify a quote. Perhaps the original sentence uses a pronoun instead of a person's name. For clarity, you might wish to include the name. Again, you cannot change the quote's meaning, and you need to signal the reader that you are modifying it slightly. You do that by using [brackets] to show exactly what you have inserted. Consider this original text:
Q237 Condoleezza Rice, President Bush's closest advisor, was speaking in New York that day. The President called and asked her to return to Washington immediately.Q
Now, let's say you want to quote only the second sentence. An exact quote wouldn't make much sense since the reader won't know whom the president was summoning. To correct that, you need to add a few words and bracket them to make it clear that you've added them to the original:
Your quote with brackets
"The President called and asked [his National Security Advisor, Condoleezza Rice] to return to Washington immediately."
That's an accurate quote even though you added several bracketed words. If you added the same words without brackets, however, it would be a misquotation.
One important rule: These additions [with brackets] . . . should not change quote's meaning in any way. The statement belongs to another writer, not to you. You're welcome to praise it or to damn it, but not to twist it.
Note: The brackets used within the above quotation are Lipson's own. I think they are meant to be illustrative, though in this context they become a bit confusing. Just to clarify, I didn't put them in. My only change was to omit a reference to an unrelated section of Lipson's book in the "One important rule section."
Hope that helps!