Old newspapers can offer a wide range of genealogical facts, stories and information. You might have to visit the library, or you might be able to search online.
It may seem a little low-tech, but old newspapers are actually a treasure trove of possible genealogical information. Don't disregard newspapers just because you think they are awkward to search or that they won't offer much beyond an obituary or two. You can get alot of information from a newspaper.
The best place to start looking for old newspapers, is actually your own local library (not necessarily the library in the area where your ancestors lived). There are searchable newspaper indexes available through inter-library networks. So you might be able to search through hundreds of papers from the library. Check with your local library and see what resources they may have.
If your family came from a very small town, then you will need to do a bit of travelling in order to access their newspaper archives. Most libraries will have archives of newspapers, though those archives are likely on microfilm or microfiche. Depending on the size of the library, you may be able to use an index to search for your ancestors names. If not, you might have to resort to scrolling through page after page of newspaper files. Still, it might be worth the effort. Many modern microfilm machines offer a print feature, so you might be able to print a direct copy of any pages that you find worthwhile. You should ask before going to the library, so you can bring enough paper and pens with you, should you have to transcribe what you find.
If you are lucky enough to have an ancestor that lived in a major city, you might even find that the newspapers you need have been digitized and are available on a searchable online database. Though more and more papers are available this way, it is still usually only the larger papers that are included.
A few places to try for online newspaper searches are: NewspaperArchive.com (pay) or Olden Times.