APA-American Psychological Association. The style of parenthetical citation is (author, year of source publication). Many professors in history, philosophy, and psychology prefer this type of format.
MLA-Modern Language Association. The style of parenthetical citation is (Author, page number). Arts & Humanities, and of course Language professors prefer thsi type of format. With this being said, it totally depends on the professor teaching the class.
Chicago Syle--a bit of a combination of the two.
Any good handbook will give many more important details, but this is a basic "run-down" of three styles.