DOI, or "direct object identifier" is a way to track articles and electronic documents on the web. Whereas the URL of a journal may change over time, the DOI for each article always stays the same.
Crossref.org is a resource for looking up DOIs based on limited citation information and, reversely, for looking up citation information based on a known DOI.
A "citation" is the way you tell your readers that certain material in your work came from another source. It also gives your readers the information necessary to find that source again, including: the author of the work, the title, the name and location of the company that published your copy of the source,the date your copy was published, the page numbers of the material you are borrowing.
This research guide will give you a brief overview of the most common citation styles and point you in the direction of more detailed resources and useful tools.
(image source: xkcd, used with permission CC by-nc)
Giving credit to the original author by citing sources is the only way to use other people's work without plagiarizing. But there are a number of other reasons to cite sources:
“What is Citation?” Plagiarism.org. Accessed February 16, 2011.