MLA (the Modern Language Association) style is most commonly used for humanities. APA (the American Psychology Association) is most commonly used for psychology and many other social sciences. Both of these styles use in-text citations of the author and page, followed by a list of works cited or references.
Chicago (Turabian) is commonly used for history. CSE (the Council of Science editors) is commonly used for sciences. Both of these styles use footnotes or endnotes, followed by a list of cited references.
We have the most common citation manuals on the bookshelf in the Center for Speaking, Writing, and the Image (CSWIM).
A great online resource for citation information is on research and documentation.
There are links to each of the above styles, along with information for how to construct in-text citations, footnotes, endnotes, and works cited/references. There are also links to sample papers, to show how all the citation information is put together.