Generally, preprints are the version of a manuscript that someone submits for publication. It has not gone through peer review or copy editing. It will not have any special formatting to match a journal, conference, or book publication. Note that not all preprints eventually get published.
Postprints are the version that has been polished up based upon reviewer and editorial feedback. But it still does not contain the formatting done by the publication in which it will eventually appear.
Eprints is used to encompass both of these, but some may apply this to other documents placed online, such as a white paper.
You may also see the version eventually provided by the publisher. Some publishers will allow authors to post this version, but may have requirements on when and where.
These are usually stored online in locations called servers or repositories.
Use this search tool to search across dozens of preprint serves. Over 2.4 million searchable items. Google Scholar also indexes several major servers.
Contains over 2.2 million documents, mostly in physics, engineering, mathematics/statistics, and computer science.
Focuses on various health sciences disciplines. Includes preprints, but also final versions. Includes other formats, including full text of journal articles.
Covers multiple discipline. Search covers multiple formats, be sure to look below search box for option to limit to 68,000+ preprints. Includes multiple other formats.
See an extensive list of repositories/servers in this Wikipedia article.
Many colleges and universities have their own institutional repositories in which their researchers may deposit preprints/postprints. Below are links to some major repositories. Note these repositories include many different formats in addition to preprints/postprints.