Copyright issues and the public domain can get a little fuzzy, but there is one super important thing to keep in mind while determining public domain status:
Other works might be in the public domain in the U.S. — consult this table from the University of California for some criteria.
Interestingly, the rules vary by country — something in the public domain in Canada might not yet be in the public domain in the U.S. Check out the Wikipedia page for List of Countries' copyright lengths for a breakdown of how the rules differ across the globe.
Image: Old Man with a Gold Chain by Rembrandt Harmensz. van Rijn, via the Art Institute of Chicago (lightly remixed)
So glad you asked! It's pretty much on a case-by-case basis, and there is no easy guidelines to tell whether or not infringement has taken place.
Fair use means that you get a legal OK to use copyright works under very specific conditions. The U.S. Copyright Act uses four key criteria to determine if a use is fair, or if it's copyright infringement:
To get a little deeper into the subject, head to the U.S. Copyright Fair Use Index, a government website that discusses various court decisions related to fair use principles. The website is also the source of all the information above.
You may have heard the term "creative commons" used in reference to creative works. Creative Commons is a non-profit that promotes open culture and has popularized the use of "creative commons licenses." These licenses generally mean the same thing — that the item is available for use! — but they do differ slightly. Sometimes a license asks for specific attribution, sometimes it doesn't, and etc.