As information gets more and more available digitally, it seems that protections granted to creative people are being understood less and less. Entire essays are reproduced under the claims of "fair use" and legally copyrighted films and songs are being sold under the claims of "public domain" just because members of the public have access to the works.
Both of these examples are illegal.
What is public domain?
A previously-copyrighted item (book, film, song, etc.) enters the status of "public domain" either when the copyright period expires or the owner of the copyright forfeits it and allows it to become public domain. Periods of copyright have changed over the years, so one cannot say exactly what rules apply to what property without researching the copyright records of each specific item. Also, the owner can apply for additional periods of copyright protection -- further muddying the waters as to when a property becomes public. (The copyright law changed in 1978, also complicating matters.)
Generally speaking, the standard copyright policy in effect today in America grants protection for a period of 70 years after the death of the creator of that work. So, if I create something today (in 2010) and live for another 50 years, the copyright for that work would expire in 2130 (70 years after my death). If I create something today and live only another 10 years, it would expire in 2090.
What is fair use?
Public domain should not be at all confused with "fair use" which is a segment of copyright law that allows a VERY SMALL excerpt from a work to be reproduced when accompanying something like a critical review or research paper. Many people claim fair use when they reproduce an entire newspaper article, or film. This is not fair use: it is copyright infringement (even if the person properly credits the author and source of the material). It is illegal unless specific permission has been granted by the creator of the work.
So, if you are analyzing a book, and you reprint a sample paragraph of that book to provide your readers a taste of what it has to offer, that is fair use. If, however, you write a song as an "homage" to a songwriter you admire and use virtually all the words or melody of another song as part of your song, that is illegal.
There are many exceptions to the general rules outlined above. If you want further clarification, you should peruse the actual copyright law here.