Internal Citation examples
You should NOT follow a quotation with a citation that includes an author's name and page number in parenthesis despite what your handbook says about doing so. In other words you should NOT have an entry like this following a quotation (Adams, 12). You should have an entry like this: (12).
But let me spell all of this out in more detail:
On first reference--typically in the sentence leading up to your quote--you should refer to A) who is speaking (the author), B) from what (the name of the essay or title of the book), and C) provide enough context of the author's discussion for the quotation to be clearly understood by the reader who may or may not have read the article that you're quoting from (possibly a brief summary of what the author is talking about or clarifying what he or she means by terms used in the quote would be appropriate). So, for example these statements might work:
In Betsy Schmimmel's essay "The Death of Dogs," Schmimmel discusses the death of her dog, Rover, saying, "he whimpered, stumbled, whimpered, stumbled, and collapsed at my feet" (19).
According to the FBI's website, "9 out of 10 police officers have smoked marijuana."
(Note that the FBI's website quote covered author and source in one fell swoop--the author is the FBI and the source is their website, so combining the two makes sense. Also note, that no page number needed to follow a web site. Finally, note that while quote #1 required a clear context--we needed to know that Schmimmel was talking about her dog for the quotation to make sense--the second did not require such a clear context because the statement makes sense on its own).
Second and Following References
On any reference following the first one, you should still provide any context necessary for the quote to make sense and also refer to who is speaking still by their last name only. The only reason to refer to anything other than the author is if A) you're using two sources by the same author or B) there is no known author for your work.
Examples of any reference after the first reference:
Schmimmel goes on to describe her grieving process: "I cried and cried and cried and cried... until I stopped" (21).
The FBI's web site also refers to these officers as "reefer monkeys."
Examples of situation A:
In another essay by Schmimmel "The Death of My Kitty," she decribes the death of her cat, "she just fell down dead. Boom! Just like that!" (11).
Examples of situation B:
In "Death of a Travelling Nursery School Teacher," the author tells the story of Nancy, a nursery school teacher. The story ends with her death at school and the reaction of one of her students: "Nancy whirled around as all the children watched. 'That's what you get from smoking pot!' Arnold cried gleefully!" (91).
Quotes within quotes
Sometimes an author will quote someone else, and you'll want to quote their quotation. For example, perhaps in a text by Martin Luther King, you find something like this:
Adolph Hitler was clearly an idiot. In fact Hitler said this quite plainly in Mein Kampf, stating that "I am an idiot" (32).
Now, what you're interested in quoting here is not all of King's discussion but what King said that Hitler said. So, your internal citation will look something like this:
In Martin Luther King's essay "What I Think of Hitler," King quotes Adolph Hitler saying of himself, "I am an idiot" (91).
Note that the page number is different. This is because Hitler is quoted on page 92 of King's essay "What I Think of Hitler," and that is the essay you are citing, not Mein Kampf. The quote from Mein Kampf is from page 32 of that book but that doesn't matter because the source you are looking at is King's essay.
Thus on your Works Cited page, you will cite King, not Hitler:
King, Martin Luther. "What I Think of Hitler." Selected Essays of Martin Luther King. Ed. Jim Y. Brown. New York: Random House, 1984. 77-98.
For further examples, check the library. Find articles written in MLA and see how those folks cite things. Your own journals also provide clear examples of how citation works (albeit in different formats like footnoting), but the principles are often the same. All your journal articles (not magazine, newspaper, etc.) can serve as models for this paper. Journal articles are argumentative research papers. So, if you feel confused about format or the purpose of these things, you have examples to draw on from your own research.
Example of a properly internally cited paper