A work is in public domain when it is created without coypright protection, or is is a creative work that is no longer protected by copyright. Works in the public domain may be freely used, duplicated, or disseminated by anyone
More information about the public domain is available at:
Kevin Smith, "Of Songs and Chairs"
If a work is in the public domain, then you may use sections of it without permission in your work.
The moral imperitive against plagiarism--passing off someone else's work as your own--still applies and plagiarism carries its own consequences apart from copyright infringement
Works fall into the public domain for one of three reasons:
1. the copyright term expires
2. the author failed to satisfy statutory formalities to perfect the copyright
3. it is a work of the U.S. federal government, or by employees acting in their capacity as agents of the federal government
As a general rule, most works enter the public domain because of old age--their term of copyright protection expires. This includes any work published in the United States before 1923. Another large block of works are in the public domain because they were published before 1964 and copyright was not renewed (renewal was a requirement for works published before 1978). A smaller group of works fell into the public domain because they were published without copyright notice (copyright notice was necessary for works published in the United States before March 1, 1989). No work will pass automatically into public domain (i.e., copyrights will not expire) until 2019.
Use the American Library Association's interactive tool Is It Protected by Copyright? to determine a work's likely copyright status