There are three basic ways to cite -- or refer to some other text -- in academic writing: you can quote it, paraphrase it, or summarize it. You can also allude to it for further reading, though that's not really the kind of citation your instructors are likely to want you to include in your work.
Quotation means that you reproduce the exact language of some other text inside your own, signalling either with quotation marks or block indentation that the language is not yours and using brackets and ellipses to signal any minor changes you make. You should quote whenever the language of the original -- as opposed to the basic idea or information -- matters. (Notice that this will vary a good deal by discipline: the language matters always in Literary Studies, but relatively seldom matters in Biology or the other natural sciences, where quoting is said to be appropriate only for especially "apt phrasing.")
Paraphrase means the you put the idea of the original in your own language. Often paraphrased passages include single words or phrases from the original that are especially important, which you'd use quotation marks to acknowledge, but otherwise you should be careful not to reproduce any of the language of the original passage. This is difficult, especially when you're working with complex ideas you're just beginning to wrap your head around. Our advice: read the passage careful, think about it, and maybe try explaining it to somebody, but then leave it alone for a while if you can. Then go back and see if you can write your paraphrase, keeping the original passage out of sight, at least at first. At the end of the process, though, go back to the original to check both that you have the information or idea right and that you didn't use any original language without quoting. Again, this is hard.
Summary is much like paraphrase, but here you're talking about a whole work, not just an excerpted passage. So the idea is to describe the larger project of some text as it informs some point you want to make yourself.
This is a really useful form of citation in scholarly works, though generally speaking, unless you're preparing something like an Honors thesis that you've researched exhaustively, most undergraduates aren't likely to have read widely enough about a topic to refer readers to other texts. This kind of citation often happens in a footnote and is usually phrased something like this: "For a fuller exploration of this idea, including its historical context, see..."