The two most important things to remember when including a quotation (i.e. someone else's words) into your own writing are: 1) cite your source and 2) work the quoted passage into the grammar of your own sentence.
This means that any time you reference someone else's words, you need to give credit where it's due. If you are unsure of whether something is common knowledge (ie. so obvious you don't have to cite it) or whether the idea was first raised by someone else, take the cautious approach. It's better to cite unnecessarily than to not cite at all.
When it comes to direct quotations, it's even more obvious that you must cite. This is where citation format - APA, MLA, Chicago Manual of Style, etc. - comes into play. Some instructors prefer footnotes, some endnotes, some parenthetical notation, and some a combination of the two. No matter what format your instructor wants, remember to cite your source and show where a quotation comes from!
When you find a really great quotation to support the point you are making in your writing, it's best if you can integrate it into your own sentence. Do not just lump it in on its own. For instance, Aldous Huxley writes: "Words can be like X-rays if you use them properly ," and goes on to assert that words will "go through anything." Do you see what I did there? I took the main quotation from Huxley -- "Words can be like X-rays if you use them properly -- they'll go through anything" -- and then I worked it into my own sentence.
Example Quotation: "Let me live, love, and say it well in good sentences," Sylvia Plath, The Unabridged Journals of Sylvia Plath
Example Integration: In The Unabridged Journals of Sylvia Plath, poet Plath exclaims: "Let me live, love, and say it well in good sentences," demonstrating the core importance of writing to her identity.