If you are looking for current news see the guide at http://libguides.princeton.edu/newspapers
First, if what you need in an English-language paper published between 1800 and about 1990, is it in one of the large collections of historical newspapers?
ProQuest Historical Newspapers Online
British Library Newspapers (17th-19th centuries)
World Newspaper Archive (check the "Places of Publication" tab to limit by region)
Consider cross-searching the Gale newspaper and periodical collections in Gale News Vault*
A few historical newspapers have stand-alone online archives. See this guide by country.
Didn't find what you need? Check to see if it has been digitized:
Newspaper digitization projects (ICON: International Coalition on Newspapers)
Wikipedia: list of online newspaper archives
If you can’t find digital, you probably can find microfilm. There is a list of newspapers held at Princeton in microfilm, arranged by state, at International Newspapers on Microfilm. If we do not have what you need, check Worldcat, then place an Interlibrary Loan request.
If you don’t know what newspapers were published in a particular time/place, check the references listed by country and under Frequently-asked questions.
If you need information about a paper, try Wikipedia. There are good articles on many historic papers.
If the paper was published after 1990, go to Current newspapers (Nexis Uni, Newsbank, Factiva).
Note: If you discover newspaper articles on the British Library site at http://www.britishnewspaperarchive.co.uk/, check Gale News Vault to see if you already have access to them before paying for the BL content. However, there are papers available through the British Library web site that are not yet available for American libraries to licence for their users. In that case, use Interlibrary Loan to get the articles you need.
Most of the links on these pages are to fee-based digital collections licensed for use at Princeton. If you are a student somewhere, ask your librarian what your library can provide. If you're a member of the general public, check with your public library, or see the excellent list of papers available for free on the Internet, prepared by Carol Singer at Bowling Green State University: