Zotero is free, cross-platform software that is used to collect your research in one place. Zotero not only collects citations, but also PDFs of full text articles when possible. It allows grouping of research into searchable collections while adding your own notes and tags. It can then export a bibliography in a variety of styles for your research paper!
As of version 5.0, Zotero requires both the stand alone version and a browser plugin. There is no longer a Firefox-only version.
Using your personal computer:
You will see a new button on your browser's toolbar which will save the article or web site you are currently viewing to Zotero.