There are several ways to identify public domain content.

1. The work may have a CC0 (sometimes called CC Zero) mark on it. CC0 is  a "no rights reserved" mark, which enables scientists, educators, artists and other creators and owners of copyright- or database-protected content to waive those interests and thereby place their works them as completely as possible in the public domain.

2. The work may have a Public Domain Mark on it. Creative Commons developed the Public Domain Mark to enable works that are no longer restricted by copyright to be marked as such in a standard and simple way, making them easily discoverable and available to others. 

3. The work may be hosted in a space that specialises in public domain content:
The Flickr Commons hosts a collection of photos that have no known copyright restrctions. 
The HathiTrust is a digital library of over 10 million books, all openly licensed, mostly in the public domain.
Project Gutenberg is a collection of ebooks, most of which are in the public domain. They also have a sheet music project. 
 

BEWARE (content hunting can be perilous!) 
Just because a piece of work has no copyright associated with it does not make it automatically a part of the public domain. Some works may be public domain in some jurisdictions, but not in others. And if you are unsure, you should always check with the owner/creator to be safe.