Often, you will need to follow quotations with a citation, noting who wrote the text, and on what page the quotation begins. Like this (from To Kill a Mockingbird):
"my brother Jem got his arm badly broken at the elbow" (Lee 3).
The important thing to note from above, is that there will be a period after the citation. In fact, there should always be sentence ending punctuation after a citation. Most of the time, this will be a period.
Here's the important part: because there will be punctuation after the citation, you should almost always leave off any punctuation at the quotation. For instance, in the quotation above, Harper Lee ends the sentence with a period. Since there is a period after the citation, the period after the word "elbow" is simply left off the quotation. Like this:
Here we start with the end of the sentence, as it appears in the novel.
Now we add quotation marks at the beginning, and the end. We're adding an ellipsis (the three dots) at the start too, to imply that there is more to the sentence before this word appears.
Now we add the citation. Notice that there is now a period directly before and directly after the citation, but the citation is not a complete sentence by itself.
Since we have to end the sentence after the citation, we're going to delete the period at the end of the quotation (really, it's more like we decided to stop quoting the text with the letter w, than removing a period from Harper Lee's writing).
And here's how the end of the quotation would look now that we're done making adjustments to the punctuation.
Sometimes, a sentence ends with another kind of punctuation mark that changes the tone or feeling of a sentence (like a question mark, or an exclamation point). In that case, the punctuation should be left at the end of the quotation, in addition to the period after the citation. Here's an example of how that would look, also from the beginning of To Kill a Mockingbird:
These are the punctuation marks that should be left at the end of a quotation:
Question Marks
Exclamation Points
Closing Parentheses
Closing Single Quotes