An important part of academic writing is citing your sources, so that your readers know where you got the ideas expressed in your paper. Proper citation also helps ensure that you aren't committing plagiarism.
Within your paper, you must provide properly-formated citations for any quotations or ideas that you borrow from other sources. Depending on the style that you use, these may appear as in-text citations, footnotes, or endnotes. You will also usually be expected to provide a bibliography (sometimes also called "references" or "works cited") at the end of your paper, which includes an alphabetical list of all sources that you used in the research and writing of your paper.
There are several different style guides that describe how to properly format a citation or bibliography. It's very likely that your professors will tell you which style guide they expect you to follow. If they don't tell you, it's probably a good idea to ask them if they have a preference.
The following handbooks and guides are for the the most commonly-used bibliographic formats.
You may also want to look into some kind of reference management software, which will properly create citations and bibliographies in most of these formats automatically.
The Purdue University Online Writing Lab has a helpful website describing the basics of these style manuals.